{"id":88,"date":"2024-10-30T17:56:34","date_gmt":"2024-10-30T17:56:34","guid":{"rendered":"https:\/\/homes.cs.washington.edu\/~beame\/site\/?page_id=88"},"modified":"2025-01-08T16:59:48","modified_gmt":"2025-01-08T16:59:48","slug":"publications-by-topic","status":"publish","type":"page","link":"https:\/\/homes.cs.washington.edu\/~beame\/site\/publications-by-topic\/","title":{"rendered":"Publications By Topic"},"content":{"rendered":"\n<p><a href=\"#beame-tradeoff\">Time-Space Tradeoffs<\/a>&nbsp;&nbsp;&nbsp;<a href=\"#beame-commstream\">Communication Complexity and Data Streams<\/a>&nbsp;&nbsp;&nbsp;<a href=\"#beame-verify\">Verification of Software and Hardware<\/a>&nbsp;&nbsp;&nbsp;<a href=\"#beame-proofsat\">Proof Complexity and Satisfiability<\/a>&nbsp;&nbsp;&nbsp;<a href=\"#beame-parallel\">Parallel and Distributed Computing<\/a>&nbsp;&nbsp;&nbsp;<a href=\"#beame-data\">Data Structures<\/a>&nbsp;&nbsp;&nbsp;<a href=\"#beame-circuit\">Circuit and PRAM Lower Bounds<\/a>&nbsp;&nbsp;&nbsp;<a href=\"#beame-other\">Other topics<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-tradeoff\"><strong>Time-Space Tradeoffs<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kornerup, Niels;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('296','tp_links')\" style=\"cursor:pointer;\">Quantum Time-Space Tradeoffs for Matrix Problems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_year\">2026<\/span><span class=\"tp_pub_additional_note\">, (To appear)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_296\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('296','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_296\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bkw:qmatrix-journal,<br \/>\r\ntitle = {Quantum Time-Space Tradeoffs for Matrix Problems},<br \/>\r\nauthor = {Paul Beame and Niels Kornerup and Michael Whitmeyer},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/quantum-matrix.pdf},<br \/>\r\nyear  = {2026},<br \/>\r\ndate = {2026-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nnote = {To appear},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('296','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_296\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/quantum-matrix.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/quantum-matrix.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/quantum-matrix.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('296','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kornerup, Niels<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('288','tp_links')\" style=\"cursor:pointer;\">Cumulative Memory Lower Bounds for Randomized and Quantum Computation<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">ACM Transactions on Computation Theory, <\/span><span class=\"tp_pub_additional_volume\">vol. 17, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 20:1\u201320:33, <\/span><span class=\"tp_pub_additional_year\">2025<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_288\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('288','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_288\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bk:cumulative-journal,<br \/>\r\ntitle = {Cumulative Memory Lower Bounds for Randomized and Quantum Computation},<br \/>\r\nauthor = {Paul Beame and Niels Kornerup},<br \/>\r\ndoi = {https:\/\/doi.org\/10.1145\/3728715},<br \/>\r\nyear  = {2025},<br \/>\r\ndate = {2025-01-01},<br \/>\r\nurldate = {2025-01-01},<br \/>\r\njournal = {ACM Transactions on Computation Theory},<br \/>\r\nvolume = {17},<br \/>\r\nnumber = {3},<br \/>\r\npages = {20:1\u201320:33},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('288','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_288\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.1145\/3728715\" title=\"Follow DOI:https:\/\/doi.org\/10.1145\/3728715\" target=\"_blank\">doi:https:\/\/doi.org\/10.1145\/3728715<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('288','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kornerup, Niels;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('82','tp_links')\" style=\"cursor:pointer;\">Quantum Time-Space Tradeoffs for Matrix Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Fifty-Sixth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 596\u2013607, <\/span><span class=\"tp_pub_additional_address\">Vancouver, B.C., Canada, <\/span><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_82\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('82','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_82\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bkw:qmatrix,<br \/>\r\ntitle = {Quantum Time-Space Tradeoffs for Matrix Problems},<br \/>\r\nauthor = {Paul Beame and Niels Kornerup and Michael Whitmeyer},<br \/>\r\nurl = {https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3618260.3649700\"},<br \/>\r\ndoi = {10.1145\/3618260.3649700},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-06-01},<br \/>\r\nbooktitle = {Proceedings of the Fifty-Sixth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {596\u2013607},<br \/>\r\naddress = {Vancouver, B.C., Canada},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('82','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_82\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3618260.3649700\"\" title=\"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3618260.3649700\"\" target=\"_blank\">https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3618260.3649700\"<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1145\/3618260.3649700\" title=\"Follow DOI:10.1145\/3618260.3649700\" target=\"_blank\">doi:10.1145\/3618260.3649700<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('82','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kornerup, Niels;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('83','tp_links')\" style=\"cursor:pointer;\">Quantum Time-Space Tradeoffs for Matrix Problems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/2401.05321, <\/span><span class=\"tp_pub_additional_year\">2024<\/span><span class=\"tp_pub_additional_note\">, (Earlier version: Electronic Colloquium on Computational Complexity (ECCC) TR24-011: http:\/\/eccc.weizmann.ac.il\/report\/2024\/011\/#revision1\")<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_83\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('83','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_83\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bkw:qmatrix-arxiv,<br \/>\r\ntitle = {Quantum Time-Space Tradeoffs for Matrix Problems},<br \/>\r\nauthor = {Paul Beame and Niels Kornerup and Michael Whitmeyer},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/2401.05321v3 <br \/>\r\nhttp:\/\/eccc.weizmann.acl.il\/report\/2024\/011\/#revision1},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/2401.05321},<br \/>\r\nnote = {Earlier version: Electronic Colloquium on Computational Complexity (ECCC) TR24-011: http:\/\/eccc.weizmann.ac.il\/report\/2024\/011\/#revision1\"},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('83','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_83\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/2401.05321v3\" title=\"http:\/\/arxiv.org\/abs\/2401.05321v3\" target=\"_blank\">http:\/\/arxiv.org\/abs\/2401.05321v3<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.weizmann.acl.il\/report\/2024\/011\/#revision1\" title=\"http:\/\/eccc.weizmann.acl.il\/report\/2024\/011\/#revision1\" target=\"_blank\">http:\/\/eccc.weizmann.acl.il\/report\/2024\/011\/#revision1<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('83','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kornerup, Niels<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('79','tp_links')\" style=\"cursor:pointer;\">Cumulative Memory Lower Bounds for Randomized and Quantum Computation<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Automata, Languages, and Programming: 50th International Colloquium (ICALP 2023), <\/span><span class=\"tp_pub_additional_pages\">pp. 17:1-17:20, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_79\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('79','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_79\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bk:cumulative,<br \/>\r\ntitle = {Cumulative Memory Lower Bounds for Randomized and Quantum Computation},<br \/>\r\nauthor = {Paul Beame and Niels Kornerup},<br \/>\r\nurl = {https:\/\/drops.dagstuhl.de\/opus\/volltexte\/2023\/18069\/pdf\/LIPIcs-ICALP-2023-17.pdf},<br \/>\r\ndoi = {https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2023.17},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-01-01},<br \/>\r\nbooktitle = {Automata, Languages, and Programming: 50th International Colloquium (ICALP 2023)},<br \/>\r\npages = {17:1-17:20},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('79','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_79\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/drops.dagstuhl.de\/opus\/volltexte\/2023\/18069\/pdf\/LIPIcs-ICALP-2023-17.pdf\" title=\"https:\/\/drops.dagstuhl.de\/opus\/volltexte\/2023\/18069\/pdf\/LIPIcs-ICALP-2023-17.pdf\" target=\"_blank\">https:\/\/drops.dagstuhl.de\/opus\/volltexte\/2023\/18069\/pdf\/LIPIcs-ICALP-2023-17.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2023.17\" title=\"Follow DOI:https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2023.17\" target=\"_blank\">doi:https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2023.17<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('79','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kornerup, Niels<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('81','tp_links')\" style=\"cursor:pointer;\">Cumulative Memory Lower Bounds for Randomized and Quantum Computation<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/2301.05680, <\/span><span class=\"tp_pub_additional_year\">2023<\/span><span class=\"tp_pub_additional_note\">, (Also Electronic Colloquium on Computational Complexity (ECCC) TR23-005: http:\/\/eccc.weizmann.acl.il\/report\/2023\/005\/)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_81\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('81','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_81\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bk:cumulative-arxiv,<br \/>\r\ntitle = {Cumulative Memory Lower Bounds for Randomized and Quantum Computation},<br \/>\r\nauthor = {Paul Beame and Niels Kornerup},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/2301.05680 <br \/>\r\nhttp:\/\/eccc.weizmann.acl.il\/report\/2023\/005\/},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-01-01},<br \/>\r\nurldate = {2023-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/2301.05680},<br \/>\r\nnote = {Also Electronic Colloquium on Computational Complexity (ECCC) TR23-005: http:\/\/eccc.weizmann.acl.il\/report\/2023\/005\/},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('81','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_81\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/2301.05680\" title=\"http:\/\/arxiv.org\/abs\/2301.05680\" target=\"_blank\">http:\/\/arxiv.org\/abs\/2301.05680<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.weizmann.acl.il\/report\/2023\/005\/\" title=\"http:\/\/eccc.weizmann.acl.il\/report\/2023\/005\/\" target=\"_blank\">http:\/\/eccc.weizmann.acl.il\/report\/2023\/005\/<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('81','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Gharan, Shayan Oveis;  Yang, Xin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('154','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Learning Finite Functions from \r\nRandom Evaluations, with Applications to Polynomials<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 31st Conference on Learning Theory, COLT 2018, <\/span><span class=\"tp_pub_additional_pages\">pp. 843\u2013856, <\/span><span class=\"tp_pub_additional_address\">Stockholm, Sweden, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_154\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('154','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_154\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bogy:learn,<br \/>\r\ntitle = {Time-Space Tradeoffs for Learning Finite Functions from <br \/>\r\nRandom Evaluations, with Applications to Polynomials},<br \/>\r\nauthor = {Paul Beame and Shayan Oveis Gharan and Xin Yang},<br \/>\r\nurl = {http:\/\/proceedings.mlr.press\/v75\/beame18a.pdf},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-07-01},<br \/>\r\nbooktitle = {Proceedings of the 31st Conference on Learning Theory, COLT 2018},<br \/>\r\npages = {843\u2013856},<br \/>\r\naddress = {Stockholm, Sweden},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('154','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_154\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/proceedings.mlr.press\/v75\/beame18a.pdf\" title=\"http:\/\/proceedings.mlr.press\/v75\/beame18a.pdf\" target=\"_blank\">http:\/\/proceedings.mlr.press\/v75\/beame18a.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('154','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Gharan, Shayan Oveis;  Yang, Xin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('155','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Learning Finite Functions from \r\nRandom Evaluations, with Applications to Polynomials<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR18-114, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_155\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('155','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_155\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bogy:learn-tr,<br \/>\r\ntitle = {Time-Space Tradeoffs for Learning Finite Functions from <br \/>\r\nRandom Evaluations, with Applications to Polynomials},<br \/>\r\nauthor = {Paul Beame and Shayan Oveis Gharan and Xin Yang},<br \/>\r\nurl = {http:\/\/eccc.weizmann.ac.il\/report\/2018\/114},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-01-01},<br \/>\r\nnumber = {TR18-114},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('155','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_155\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.weizmann.ac.il\/report\/2018\/114\" title=\"http:\/\/eccc.weizmann.ac.il\/report\/2018\/114\" target=\"_blank\">http:\/\/eccc.weizmann.ac.il\/report\/2018\/114<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('155','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Gharan, Shayan Oveis;  Yang, Xin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('153','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Learning from Small Test Spaces: Learning Low Degree Polynomial Functions<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1708.02640, <\/span><span class=\"tp_pub_additional_year\">2017<\/span><span class=\"tp_pub_additional_note\">, (Also July 2017 Technical Report TR17-120Electronic Colloquium on Computational Complexity available at \r\n http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/120\/index.html)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_153\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('153','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_153\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bogy:quadlearn-tr,<br \/>\r\ntitle = {Time-Space Tradeoffs for Learning from Small Test Spaces: Learning Low Degree Polynomial Functions},<br \/>\r\nauthor = {Paul Beame and Shayan Oveis Gharan and Xin Yang},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1708.02640 <br \/>\r\nhttp:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/120\/index.html},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1708.02640},<br \/>\r\nnote = {Also July 2017 Technical Report TR17-120Electronic Colloquium on Computational Complexity available at <br \/>\r\n http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/120\/index.html},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('153','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_153\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1708.02640\" title=\"http:\/\/arxiv.org\/abs\/1708.02640\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1708.02640<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/120\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/120\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/120\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('153','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Beck, Chris;  Impagliazzo, Russell<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('26','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for \r\n Superlinear Space<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 45, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 1612\u20131645, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_26\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('26','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_26\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbi:proofspace-journal,<br \/>\r\ntitle = {Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for <br \/>\r\n Superlinear Space},<br \/>\r\nauthor = {Paul Beame and Chris Beck and Russell Impagliazzo},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {45},<br \/>\r\nnumber = {4},<br \/>\r\npages = {1612\u20131645},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('26','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_26\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('26','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent;  Patrascu, Mihai<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('106','tp_links')\" style=\"cursor:pointer;\">Finding the Median (Obliviously) with Bounded Space<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1505.00090, <\/span><span class=\"tp_pub_additional_year\">2015<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_106\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('106','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_106\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{blp:median-tr,<br \/>\r\ntitle = {Finding the Median (Obliviously) with Bounded Space},<br \/>\r\nauthor = {Paul Beame and Vincent Liew and Mihai Patrascu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1505.00090},<br \/>\r\nyear  = {2015},<br \/>\r\ndate = {2015-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1505.00090},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('106','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_106\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1505.00090\" title=\"http:\/\/arxiv.org\/abs\/1505.00090\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1505.00090<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('106','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent;  Patrascu, Mihai<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('107','tp_links')\" style=\"cursor:pointer;\">Finding the Median (Obliviously) with Bounded Space<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I, <\/span><span class=\"tp_pub_additional_pages\">pp. 103\u2013115, <\/span><span class=\"tp_pub_additional_year\">2015<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_107\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('107','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_107\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{blp:median,<br \/>\r\ntitle = {Finding the Median (Obliviously) with Bounded Space},<br \/>\r\nauthor = {Paul Beame and Vincent Liew and Mihai Patrascu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icmedian.pdf},<br \/>\r\nyear  = {2015},<br \/>\r\ndate = {2015-01-01},<br \/>\r\nurldate = {2015-01-01},<br \/>\r\nbooktitle = {Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I},<br \/>\r\npages = {103\u2013115},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('107','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_107\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icmedian.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icmedian.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icmedian.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('107','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Clifford, Rapha\u00ebl;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('42','tp_links')\" style=\"cursor:pointer;\">Element Distinctness, Frequency Moments, and Sliding Windows<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 54th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 290\u2013299, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Berkeley, CA, <\/span><span class=\"tp_pub_additional_year\">2013<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_42\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('42','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_42\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bcm:windowsED,<br \/>\r\ntitle = {Element Distinctness, Frequency Moments, and Sliding Windows},<br \/>\r\nauthor = {Paul Beame and Rapha\u00ebl Clifford and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/windows.pdf},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-10-01},<br \/>\r\nbooktitle = {Proceedings 54th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {290\u2013299},<br \/>\r\naddress = {Berkeley, CA},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('42','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_42\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/windows.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/windows.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/windows.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('42','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Clifford, Rapha\u00ebl;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('43','tp_links')\" style=\"cursor:pointer;\">Element Distinctness, Frequency Moments, and Sliding Windows<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1309.3690, <\/span><span class=\"tp_pub_additional_year\">2013<\/span><span class=\"tp_pub_additional_note\">, (Also Technical Report TR13-127, Electronic Colloquium on Computational Complexity available at http:\/\/eccc.hpi-web.de\/report\/2013\/127)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_43\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('43','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_43\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bcm:windowsED-arxiv+eccc,<br \/>\r\ntitle = {Element Distinctness, Frequency Moments, and Sliding Windows},<br \/>\r\nauthor = {Paul Beame and Rapha\u00ebl Clifford and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1309.3690 <br \/>\r\nhttp:\/\/eccc.hpi-web.de\/report\/2013\/127},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-01-01},<br \/>\r\nurldate = {2013-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1309.3690},<br \/>\r\nnote = {Also Technical Report TR13-127, Electronic Colloquium on Computational Complexity available at http:\/\/eccc.hpi-web.de\/report\/2013\/127},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('43','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_43\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1309.3690\" title=\"http:\/\/arxiv.org\/abs\/1309.3690\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1309.3690<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.hpi-web.de\/report\/2013\/127\" title=\"http:\/\/eccc.hpi-web.de\/report\/2013\/127\" target=\"_blank\">http:\/\/eccc.hpi-web.de\/report\/2013\/127<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('43','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Beck, Chris;  Impagliazzo, Russell<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('25','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for \r\n Superlinear Space<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 212\u2013232, <\/span><span class=\"tp_pub_additional_address\">New York, NY, <\/span><span class=\"tp_pub_additional_year\">2012<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_25\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('25','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_25\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bbi:proofspace,<br \/>\r\ntitle = {Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for <br \/>\r\n Superlinear Space},<br \/>\r\nauthor = {Paul Beame and Chris Beck and Russell Impagliazzo},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-05-01},<br \/>\r\nbooktitle = {Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {212\u2013232},<br \/>\r\naddress = {New York, NY},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('25','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_25\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('25','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Clifford, Rapha\u00ebl;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('41','tp_links')\" style=\"cursor:pointer;\">Sliding Windows with Limited Storage<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1212.4372, <\/span><span class=\"tp_pub_additional_year\">2012<\/span><span class=\"tp_pub_additional_note\">, (Also Technical Report TR12-178, Electronic Colloquium on Computational Complexity available at http:\/\/eccc.uni-trier.de\/eccc-reports\/2012\/TR12-178\/index.html)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_41\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('41','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_41\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bcm:windows-arxiv+eccc,<br \/>\r\ntitle = {Sliding Windows with Limited Storage},<br \/>\r\nauthor = {Paul Beame and Rapha\u00ebl Clifford and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1212.4372 <br \/>\r\nhttp:\/\/eccc.uni-trier.de\/eccc-reports\/2012\/TR12-178\/index.html},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-01-01},<br \/>\r\nurldate = {2012-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1212.4372},<br \/>\r\nnote = {Also Technical Report TR12-178, Electronic Colloquium on Computational Complexity available at http:\/\/eccc.uni-trier.de\/eccc-reports\/2012\/TR12-178\/index.html},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('41','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_41\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1212.4372\" title=\"http:\/\/arxiv.org\/abs\/1212.4372\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1212.4372<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2012\/TR12-178\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2012\/TR12-178\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2012\/TR12-178\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('41','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Beck, Chris;  Impagliazzo, Russell<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('24','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for \r\n Superlinear Space<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR11-149, <\/span><span class=\"tp_pub_additional_year\">2011<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_24\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('24','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_24\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bbi:proofspace-eccc,<br \/>\r\ntitle = {Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for <br \/>\r\n Superlinear Space},<br \/>\r\nauthor = {Paul Beame and Chris Beck and Russell Impagliazzo},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf},<br \/>\r\nyear  = {2011},<br \/>\r\ndate = {2011-11-01},<br \/>\r\nnumber = {TR11-149},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('24','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_24\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('24','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('116','tp_links')\" style=\"cursor:pointer;\">Making Branching Programs Oblivious Requires Superlogarithmic \r\n Overhead<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings Twenty-Sixth Annual IEEE Conference on Computational Complexity, <\/span><span class=\"tp_pub_additional_pages\">pp. 12\u201322, <\/span><span class=\"tp_pub_additional_address\">San Jose, CA, <\/span><span class=\"tp_pub_additional_year\">2011<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_116\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('116','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_116\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bm:robp,<br \/>\r\ntitle = {Making Branching Programs Oblivious Requires Superlogarithmic <br \/>\r\n Overhead},<br \/>\r\nauthor = {Paul Beame and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/robp-ccc.pdf},<br \/>\r\nyear  = {2011},<br \/>\r\ndate = {2011-06-01},<br \/>\r\nbooktitle = {Proceedings Twenty-Sixth Annual IEEE Conference on Computational Complexity},<br \/>\r\npages = {12\u201322},<br \/>\r\naddress = {San Jose, CA},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('116','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_116\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/robp-ccc.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/robp-ccc.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/robp-ccc.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('116','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Saks, Michael;  Sun, Xiaodong;  Vee, Erik<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('137','tp_links')\" style=\"cursor:pointer;\">Time-Space Trade-Off Lower Bounds for Randomized Computation of \r\n Decision Problems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of the ACM, <\/span><span class=\"tp_pub_additional_volume\">vol. 50, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 154\u2013195, <\/span><span class=\"tp_pub_additional_year\">2003<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_137\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('137','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_137\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bssv:randomts-journal,<br \/>\r\ntitle = {Time-Space Trade-Off Lower Bounds for Randomized Computation of <br \/>\r\n Decision Problems},<br \/>\r\nauthor = {Paul Beame and Michael Saks and Xiaodong Sun and Erik Vee},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomts.pdf},<br \/>\r\nyear  = {2003},<br \/>\r\ndate = {2003-01-01},<br \/>\r\njournal = {Journal of the ACM},<br \/>\r\nvolume = {50},<br \/>\r\nnumber = {2},<br \/>\r\npages = {154\u2013195},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('137','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_137\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomts.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomts.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomts.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('137','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Vee, Erik<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('165','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs, Multiparty Communication \r\n Complexity, and Nearest-Neighbor Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 688-697, <\/span><span class=\"tp_pub_additional_address\">Montreal, Quebec, Canada, <\/span><span class=\"tp_pub_additional_year\">2002<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_165\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('165','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_165\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bv:multibp,<br \/>\r\ntitle = {Time-Space Tradeoffs, Multiparty Communication <br \/>\r\n Complexity, and Nearest-Neighbor Problems},<br \/>\r\nauthor = {Paul Beame and Erik Vee},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf},<br \/>\r\nyear  = {2002},<br \/>\r\ndate = {2002-05-01},<br \/>\r\nurldate = {2002-05-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {688-697},<br \/>\r\naddress = {Montreal, Quebec, Canada},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('165','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_165\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('165','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Jayram, T. S.;  Saks, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('139','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Branching Programs<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Computer and System Sciences, <\/span><span class=\"tp_pub_additional_volume\">vol. 63, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 542\u2013572, <\/span><span class=\"tp_pub_additional_year\">2001<\/span><span class=\"tp_pub_additional_note\">, (Special issue of selected papers from 1998 FOCS Conference)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_139\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('139','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_139\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bst:tradeoff-journal,<br \/>\r\ntitle = {Time-Space Tradeoffs for Branching Programs},<br \/>\r\nauthor = {Paul Beame and T. S. Jayram and Michael Saks},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch.pdf},<br \/>\r\nyear  = {2001},<br \/>\r\ndate = {2001-12-01},<br \/>\r\njournal = {Journal of Computer and System Sciences},<br \/>\r\nvolume = {63},<br \/>\r\nnumber = {4},<br \/>\r\npages = {542\u2013572},<br \/>\r\nnote = {Special issue of selected papers from 1998 FOCS Conference},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('139','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_139\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('139','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Saks, Michael;  Sun, Xiaodong;  Vee, Erik<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('136','tp_links')\" style=\"cursor:pointer;\">Super-linear Time-Space Tradeoff Lower Bounds for Randomized Computation<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 41st Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 169\u2013179, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Redondo Beach, CA, <\/span><span class=\"tp_pub_additional_year\">2000<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_136\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('136','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_136\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bssv:randomts-focs,<br \/>\r\ntitle = {Super-linear Time-Space Tradeoff Lower Bounds for Randomized Computation},<br \/>\r\nauthor = {Paul Beame and Michael Saks and Xiaodong Sun and Erik Vee},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/superlinear.pdf},<br \/>\r\nyear  = {2000},<br \/>\r\ndate = {2000-11-01},<br \/>\r\nbooktitle = {Proceedings 41st Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {169\u2013179},<br \/>\r\naddress = {Redondo Beach, CA},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('136','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_136\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/superlinear.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/superlinear.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/superlinear.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('136','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Saks, Michael;  Sun, Xiaodong;  Vee, Erik<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('135','tp_links')\" style=\"cursor:pointer;\">Super-linear Time-Space Tradeoff Lower Bounds for Randomized Computation<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR00-025, <\/span><span class=\"tp_pub_additional_year\">2000<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_135\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('135','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_135\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bssv:randomts-eccc,<br \/>\r\ntitle = {Super-linear Time-Space Tradeoff Lower Bounds for Randomized Computation},<br \/>\r\nauthor = {Paul Beame and Michael Saks and Xiaodong Sun and Erik Vee},<br \/>\r\nurl = {http:\/\/eccc.uni-trier.de\/eccc-reports\/2000\/TR00-025\/index.html},<br \/>\r\nyear  = {2000},<br \/>\r\ndate = {2000-01-01},<br \/>\r\nnumber = {TR00-025},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('135','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_135\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2000\/TR00-025\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2000\/TR00-025\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2000\/TR00-025\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('135','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Borodin, Allan;  Raghavan, Prabhakar;  Ruzzo, Walter L.;  Tompa, Martin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('34','tp_links')\" style=\"cursor:pointer;\">A Time-Space Tradeoff for Undirected Graph Traversal by \r\n Walking Automata<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 28, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 1051\u20131072, <\/span><span class=\"tp_pub_additional_year\">1999<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_34\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('34','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_34\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbrrt:wag,<br \/>\r\ntitle = {A Time-Space Tradeoff for Undirected Graph Traversal by <br \/>\r\n Walking Automata},<br \/>\r\nauthor = {Paul Beame and Allan Borodin and Prabhakar Raghavan and Walter L. Ruzzo and Martin Tompa},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wag.pdf},<br \/>\r\nyear  = {1999},<br \/>\r\ndate = {1999-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {28},<br \/>\r\nnumber = {3},<br \/>\r\npages = {1051\u20131072},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('34','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_34\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wag.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wag.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wag.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('34','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Saks, Michael;  Thathachar, Jayram S.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('138','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Branching Programs<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 39th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 254-263, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Palo Alto, CA, <\/span><span class=\"tp_pub_additional_year\">1998<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_138\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('138','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_138\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bst:tradeoff,<br \/>\r\ntitle = {Time-Space Tradeoffs for Branching Programs},<br \/>\r\nauthor = {Paul Beame and Michael Saks and Jayram S. Thathachar},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbranch.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-11-01},<br \/>\r\nbooktitle = {Proceedings 39th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {254-263},<br \/>\r\naddress = {Palo Alto, CA},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('138','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_138\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbranch.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbranch.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbranch.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('138','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Saks, Michael;  Thathachar, Jayram S.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('164','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Branching Programs<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR98-053, <\/span><span class=\"tp_pub_additional_year\">1998<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_164\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('164','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_164\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bst:tradeoff-eccc,<br \/>\r\ntitle = {Time-Space Tradeoffs for Branching Programs},<br \/>\r\nauthor = {Paul Beame and Michael Saks and Jayram S. Thathachar},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch-eccc.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-01-01},<br \/>\r\nnumber = {TR98-053},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('164','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_164\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch-eccc.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch-eccc.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/branch-eccc.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('164','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Borodin, Allan;  Raghavan, Prabhakar;  Ruzzo, Walter L.;  Tompa, Martin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('35','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Undirected Graph Traversal by Graph Automata<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Information and Computation, <\/span><span class=\"tp_pub_additional_volume\">vol. 130, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 101-129, <\/span><span class=\"tp_pub_additional_year\">1996<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_35\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('35','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_35\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbrrt:ag,<br \/>\r\ntitle = {Time-Space Tradeoffs for Undirected Graph Traversal by Graph Automata},<br \/>\r\nauthor = {Paul Beame and Allan Borodin and Prabhakar Raghavan and Walter L. Ruzzo and Martin Tompa},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ag.pdf},<br \/>\r\nyear  = {1996},<br \/>\r\ndate = {1996-11-01},<br \/>\r\njournal = {Information and Computation},<br \/>\r\nvolume = {130},<br \/>\r\nnumber = {2},<br \/>\r\npages = {101-129},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('35','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_35\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ag.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ag.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ag.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('35','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Tompa, Martin;  Yan, Peiyuan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('143','tp_links')\" style=\"cursor:pointer;\">Communication-Space Tradeoffs for Unrestricted Protocols<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 23, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 652-661, <\/span><span class=\"tp_pub_additional_year\">1994<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_143\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('143','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_143\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bty:communication,<br \/>\r\ntitle = {Communication-Space Tradeoffs for Unrestricted Protocols},<br \/>\r\nauthor = {Paul Beame and Martin Tompa and Peiyuan Yan},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf},<br \/>\r\nyear  = {1994},<br \/>\r\ndate = {1994-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {23},<br \/>\r\nnumber = {3},<br \/>\r\npages = {652-661},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('143','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_143\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('143','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Borodin, Allan;  Raghavan, Prabhakar;  Ruzzo, Walter L.;  Tompa, Martin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('33','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Undirected Graph Traversal<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Department of Computer Science and Engineering, University of Washington <\/span><span class=\"tp_pub_additional_number\">no. UW-CSE-93\u201302\u201301, <\/span><span class=\"tp_pub_additional_year\">1993<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_33\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('33','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_33\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bbrrt:jagtr,<br \/>\r\ntitle = {Time-Space Tradeoffs for Undirected Graph Traversal},<br \/>\r\nauthor = {Paul Beame and Allan Borodin and Prabhakar Raghavan and Walter L. Ruzzo and Martin Tompa},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/bag.ps},<br \/>\r\nyear  = {1993},<br \/>\r\ndate = {1993-02-01},<br \/>\r\nnumber = {UW-CSE-93\u201302\u201301},<br \/>\r\ninstitution = {Department of Computer Science and Engineering, University of Washington},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('33','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_33\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/bag.ps\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/bag.ps\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/bag.ps<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('33','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('19','tp_links')\" style=\"cursor:pointer;\">A General Sequential Time-Space Tradeoff for Finding Unique Elements<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 20, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 270-277, <\/span><span class=\"tp_pub_additional_year\">1991<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_19\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('19','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_19\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bea:sorting,<br \/>\r\ntitle = {A General Sequential Time-Space Tradeoff for Finding Unique Elements},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sorting.pdf},<br \/>\r\nyear  = {1991},<br \/>\r\ndate = {1991-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {20},<br \/>\r\nnumber = {2},<br \/>\r\npages = {270-277},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('19','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_19\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sorting.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sorting.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sorting.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('19','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Borodin, Allan;  Raghavan, Prabhakar;  Ruzzo, Walter L.;  Tompa, Martin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('32','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs for Undirected Graph Traversal<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 31st Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 429-438, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">St. Louis, MO, <\/span><span class=\"tp_pub_additional_year\">1990<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_32\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('32','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_32\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bbrrt:jag-focs,<br \/>\r\ntitle = {Time-Space Tradeoffs for Undirected Graph Traversal},<br \/>\r\nauthor = {Paul Beame and Allan Borodin and Prabhakar Raghavan and Walter L. Ruzzo and Martin Tompa},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbags.pdf},<br \/>\r\nyear  = {1990},<br \/>\r\ndate = {1990-10-01},<br \/>\r\nbooktitle = {Proceedings 31st Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {429-438},<br \/>\r\naddress = {St. Louis, MO},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('32','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_32\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbags.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbags.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsbags.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('32','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Tompa, Martin;  Yan, Peiyuan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('141','tp_links')\" style=\"cursor:pointer;\">Communication-Space Tradeoffs for Unrestricted Protocols<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 31st Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 420-428, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">St. Louis, MO, <\/span><span class=\"tp_pub_additional_year\">1990<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_141\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('141','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_141\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bty:communication-focs,<br \/>\r\ntitle = {Communication-Space Tradeoffs for Unrestricted Protocols},<br \/>\r\nauthor = {Paul Beame and Martin Tompa and Peiyuan Yan},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focscommspace.pdf},<br \/>\r\nyear  = {1990},<br \/>\r\ndate = {1990-10-01},<br \/>\r\nbooktitle = {Proceedings 31st Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {420-428},<br \/>\r\naddress = {St. Louis, MO},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('141','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_141\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focscommspace.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focscommspace.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focscommspace.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('141','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('16','tp_links')\" style=\"cursor:pointer;\">A General Sequential Time-Space Tradeoff for Finding Unique Elements<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 197-203, <\/span><span class=\"tp_pub_additional_address\">Seattle, WA, <\/span><span class=\"tp_pub_additional_year\">1989<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_16\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('16','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_16\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bea89,<br \/>\r\ntitle = {A General Sequential Time-Space Tradeoff for Finding Unique Elements},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsorting.pdf},<br \/>\r\nyear  = {1989},<br \/>\r\ndate = {1989-05-01},<br \/>\r\nbooktitle = {Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {197-203},<br \/>\r\naddress = {Seattle, WA},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('16','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_16\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsorting.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsorting.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsorting.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('16','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-commstream\"><strong>Communication Complexity and Data Streams<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('293','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR25-057, <\/span><span class=\"tp_pub_additional_year\">2025<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_293\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('293','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_293\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bw:multiparty-collision-eccc,<br \/>\r\ntitle = {Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles},<br \/>\r\nauthor = {Paul Beame and Michael Whitmeyer},<br \/>\r\nurl = {https:\/\/eccc.weizmann.ac.il\/report\/2025\/057},<br \/>\r\nyear  = {2025},<br \/>\r\ndate = {2025-01-01},<br \/>\r\nnumber = {TR25-057},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('293','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_293\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/eccc.weizmann.ac.il\/report\/2025\/057\" title=\"https:\/\/eccc.weizmann.ac.il\/report\/2025\/057\" target=\"_blank\">https:\/\/eccc.weizmann.ac.il\/report\/2025\/057<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('293','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('294','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Automata, Languages, and Programming: 52nd International Colloquium (ICALP 2025), <\/span><span class=\"tp_pub_additional_pages\">pp. 21:1\u201321:20, <\/span><span class=\"tp_pub_additional_year\">2025<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_294\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('294','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_294\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bw:multiparty-collision,<br \/>\r\ntitle = {Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles},<br \/>\r\nauthor = {Paul Beame and Michael Whitmeyer},<br \/>\r\nurl = {https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf},<br \/>\r\ndoi = {10.4230\/LIPICS.ICALP.2025.21},<br \/>\r\nyear  = {2025},<br \/>\r\ndate = {2025-01-01},<br \/>\r\nurldate = {2025-01-01},<br \/>\r\nbooktitle = {Automata, Languages, and Programming: 52nd International Colloquium (ICALP 2025)},<br \/>\r\nvolume = {334},<br \/>\r\npages = {21:1\u201321:20},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('294','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_294\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf\" title=\"https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf\" target=\"_blank\">https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.4230\/LIPICS.ICALP.2025.21\" title=\"Follow DOI:10.4230\/LIPICS.ICALP.2025.21\" target=\"_blank\">doi:10.4230\/LIPICS.ICALP.2025.21<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('294','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('292','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity of Collision-Finding<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">arxiv\/math.co <\/span><span class=\"tp_pub_additional_number\">no. arXiv:2411.07400, <\/span><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_292\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('292','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_292\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bw:multiparty-collision-arxiv,<br \/>\r\ntitle = {Multiparty Communication Complexity of Collision-Finding},<br \/>\r\nauthor = {Paul Beame and Michael Whitmeyer},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/2411.07400},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-01-01},<br \/>\r\nnumber = {arXiv:2411.07400},<br \/>\r\ninstitution = {arxiv\/math.co},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('292','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_292\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/2411.07400\" title=\"http:\/\/arxiv.org\/abs\/2411.07400\" target=\"_blank\">http:\/\/arxiv.org\/abs\/2411.07400<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('292','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koroth, Sajin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('87','tp_links')\" style=\"cursor:pointer;\">On Disperser\/Lifting Properties of the Index and Inner-Product Functions<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">14th Innovations in Theoretical Computer Science Conference, ITCS \r\n 2023, January 10\u201313, 2023, Cambridge, MA, USA, <\/span><span class=\"tp_pub_additional_pages\">pp. 14:1-14:17, <\/span><span class=\"tp_pub_additional_publisher\">Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_87\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('87','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_87\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bk:lift-itcs,<br \/>\r\ntitle = {On Disperser\/Lifting Properties of the Index and Inner-Product Functions},<br \/>\r\nauthor = {Paul Beame and Sajin Koroth},<br \/>\r\ndoi = {https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-01-01},<br \/>\r\nbooktitle = {14th Innovations in Theoretical Computer Science Conference, ITCS <br \/>\r\n 2023, January 10\u201313, 2023, Cambridge, MA, USA},<br \/>\r\nvolume = {251},<br \/>\r\npages = {14:1-14:17},<br \/>\r\npublisher = {Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik},<br \/>\r\nseries = {LIPIcs},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('87','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_87\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14\" title=\"Follow DOI:https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14\" target=\"_blank\">doi:https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('87','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koroth, Sajin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('86','tp_links')\" style=\"cursor:pointer;\">On Disperser\/Lifting Properties of the Index and Inner-Product Functions<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/2211.17211, <\/span><span class=\"tp_pub_additional_year\">2022<\/span><span class=\"tp_pub_additional_note\">, (ECCC Technical Report TR22-173 http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_86\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('86','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_86\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bk:lift-tr,<br \/>\r\ntitle = {On Disperser\/Lifting Properties of the Index and Inner-Product Functions},<br \/>\r\nauthor = {Paul Beame and Sajin Koroth},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/2211.17211 <br \/>\r\nhttp:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html},<br \/>\r\nyear  = {2022},<br \/>\r\ndate = {2022-01-01},<br \/>\r\nurldate = {2022-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/2211.17211},<br \/>\r\nnote = {ECCC Technical Report TR22-173 http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('86','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_86\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/2211.17211\" title=\"http:\/\/arxiv.org\/abs\/2211.17211\" target=\"_blank\">http:\/\/arxiv.org\/abs\/2211.17211<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html\" title=\"http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html\" target=\"_blank\">http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('86','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('92','tp_links')\" style=\"cursor:pointer;\">Communication Steps for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of the ACM, <\/span><span class=\"tp_pub_additional_volume\">vol. 64, <\/span><span class=\"tp_pub_additional_number\">no. 6, <\/span><span class=\"tp_pub_additional_pages\">pp. 40:1-58, <\/span><span class=\"tp_pub_additional_year\">2017<\/span><span class=\"tp_pub_additional_note\">, (Preliminary material in Proceedings of 2013 and 2014 ACM Symposium on Principles of Database Systems.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_92\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('92','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_92\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:mpc-journal,<br \/>\r\ntitle = {Communication Steps for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-10-01},<br \/>\r\njournal = {Journal of the ACM},<br \/>\r\nvolume = {64},<br \/>\r\nnumber = {6},<br \/>\r\npages = {40:1-58},<br \/>\r\nnote = {Preliminary material in Proceedings of 2013 and 2014 ACM Symposium on Principles of Database Systems.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('92','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_92\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('92','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Rashtchian, Cyrus<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('159','tp_links')\" style=\"cursor:pointer;\">Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, <\/span><span class=\"tp_pub_additional_pages\">pp. 289\u2013306, <\/span><span class=\"tp_pub_additional_address\">Barcelona, ES, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_159\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('159','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_159\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{br:simjoin,<br \/>\r\ntitle = {Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube},<br \/>\r\nauthor = {Paul Beame and Cyrus Rashtchian},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\nbooktitle = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms},<br \/>\r\npages = {289\u2013306},<br \/>\r\naddress = {Barcelona, ES},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('159','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_159\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('159','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Rashtchian, Cyrus<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('160','tp_links')\" style=\"cursor:pointer;\">Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1611.04999, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_160\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('160','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_160\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{br:simjoin-tr,<br \/>\r\ntitle = {Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube},<br \/>\r\nauthor = {Paul Beame and Cyrus Rashtchian},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1611.04999},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-11-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1611.04999},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('160','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_160\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1611.04999\" title=\"http:\/\/arxiv.org\/abs\/1611.04999\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1611.04999<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('160','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Koutris, Paraschos;  Beame, Paul;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('169','tp_links')\" style=\"cursor:pointer;\">Worst-Case Optimal Algorithms for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of 19th International Conference on Database Theory, <\/span><span class=\"tp_pub_additional_pages\">pp. 8:1\u20138:18, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_169\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('169','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_169\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{kbs:worst,<br \/>\r\ntitle = {Worst-Case Optimal Algorithms for Parallel Query Processing},<br \/>\r\nauthor = {Paraschos Koutris and Paul Beame and Dan Suciu},<br \/>\r\nurl = {http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-03-01},<br \/>\r\nbooktitle = {Proceedings of 19th International Conference on Database Theory},<br \/>\r\npages = {8:1\u20138:18},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('169','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_169\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8\" title=\"http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8\" target=\"_blank\">http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('169','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('97','tp_links')\" style=\"cursor:pointer;\">Communication Cost in Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1602.06236, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_97\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('97','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_97\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:cost-arxiv,<br \/>\r\ntitle = {Communication Cost in Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1602.06236},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1602.06236},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('97','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_97\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1602.06236\" title=\"http:\/\/arxiv.org\/abs\/1602.06236\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1602.06236<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('97','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('98','tp_links')\" style=\"cursor:pointer;\">Worst-Case Optimal Algorithms for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1604.01848, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_98\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('98','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_98\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:worst-arxiv,<br \/>\r\ntitle = {Worst-Case Optimal Algorithms for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1604.01848},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1604.01848},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('98','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_98\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1604.01848\" title=\"http:\/\/arxiv.org\/abs\/1604.01848\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1604.01848<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('98','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('94','tp_links')\" style=\"cursor:pointer;\">Skew in Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Third Annual ACM Symposium on Principles of Database Systems, <\/span><span class=\"tp_pub_additional_pages\">pp. 212\u2013223, <\/span><span class=\"tp_pub_additional_address\">Snowbird, UT, <\/span><span class=\"tp_pub_additional_year\">2014<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_94\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('94','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_94\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bks:skew-pods,<br \/>\r\ntitle = {Skew in Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558},<br \/>\r\nyear  = {2014},<br \/>\r\ndate = {2014-06-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Third Annual ACM Symposium on Principles of Database Systems},<br \/>\r\npages = {212\u2013223},<br \/>\r\naddress = {Snowbird, UT},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('94','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_94\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558\" title=\"https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558\" target=\"_blank\">https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('94','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('95','tp_links')\" style=\"cursor:pointer;\">Skew in Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1401.1872, <\/span><span class=\"tp_pub_additional_year\">2014<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_95\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('95','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_95\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:skew-arxiv,<br \/>\r\ntitle = {Skew in Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1401.1872},<br \/>\r\nyear  = {2014},<br \/>\r\ndate = {2014-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1401.1872},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('95','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_95\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1401.1872\" title=\"http:\/\/arxiv.org\/abs\/1401.1872\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1401.1872<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('95','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('93','tp_links')\" style=\"cursor:pointer;\">Communication Steps for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Second Annual ACM Symposium on Principles of Database Systems, <\/span><span class=\"tp_pub_additional_pages\">pp. 273\u2013284, <\/span><span class=\"tp_pub_additional_address\">New York, NY, <\/span><span class=\"tp_pub_additional_year\">2013<\/span><span class=\"tp_pub_additional_note\">, (Winner of 2023 ACM PODS Alberto O. Mendelzon Test-of-Time Award.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_93\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('93','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_93\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bks:mpc-pods,<br \/>\r\ntitle = {Communication Steps for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-06-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Second Annual ACM Symposium on Principles of Database Systems},<br \/>\r\npages = {273\u2013284},<br \/>\r\naddress = {New York, NY},<br \/>\r\nnote = {Winner of 2023 ACM PODS Alberto O. Mendelzon Test-of-Time Award.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('93','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_93\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('93','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('96','tp_links')\" style=\"cursor:pointer;\">Communication Steps for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1306.5972, <\/span><span class=\"tp_pub_additional_year\">2013<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_96\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('96','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_96\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:mpc-arxiv,<br \/>\r\ntitle = {Communication Steps for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1306.5972},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-01-01},<br \/>\r\nurldate = {2013-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1306.5972},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('96','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_96\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1306.5972\" title=\"http:\/\/arxiv.org\/abs\/1306.5972\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1306.5972<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('96','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh, Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('65','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 41, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 484\u2013518, <\/span><span class=\"tp_pub_additional_year\">2012<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_65\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('65','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_65\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bh:multiparty-journal,<br \/>\r\ntitle = {Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Trinh Huynh},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {41},<br \/>\r\nnumber = {3},<br \/>\r\npages = {484\u2013518},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('65','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_65\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('65','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh, Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('61','tp_links')\" style=\"cursor:pointer;\">On the Value of Multiple Read\/Write Streams for Approximating Frequency Moments<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">ACM Transactions on Computation Theory, <\/span><span class=\"tp_pub_additional_volume\">vol. 3, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 6.1\u20136.22, <\/span><span class=\"tp_pub_additional_year\">2011<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_61\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('61','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_61\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bh:freq-journal,<br \/>\r\ntitle = {On the Value of Multiple Read\/Write Streams for Approximating Frequency Moments},<br \/>\r\nauthor = {Paul Beame and Trinh Huynh},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freqjournal.pdf},<br \/>\r\nyear  = {2011},<br \/>\r\ndate = {2011-01-01},<br \/>\r\njournal = {ACM Transactions on Computation Theory},<br \/>\r\nvolume = {3},<br \/>\r\nnumber = {2},<br \/>\r\npages = {6.1\u20136.22},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('61','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_61\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freqjournal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freqjournal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freqjournal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('61','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  David, Matei;  Pitassi, Toniann;  Woelfel, Philipp<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('52','tp_links')\" style=\"cursor:pointer;\">Separating Deterministic from Randomized Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Theory of Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 6, <\/span><span class=\"tp_pub_additional_pages\">pp. 201\u2013225, <\/span><span class=\"tp_pub_additional_year\">2010<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_52\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('52','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_52\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bdpw:kparty-journal,<br \/>\r\ntitle = {Separating Deterministic from Randomized Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Matei David and Toniann Pitassi and Philipp Woelfel},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kparty.pdf},<br \/>\r\nyear  = {2010},<br \/>\r\ndate = {2010-01-01},<br \/>\r\njournal = {Theory of Computing},<br \/>\r\nvolume = {6},<br \/>\r\npages = {201\u2013225},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('52','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_52\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kparty.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kparty.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kparty.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('52','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh-Ngoc, Dang-Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('64','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 50th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 53\u201362, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Atlanta, GA, <\/span><span class=\"tp_pub_additional_year\">2009<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_64\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('64','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_64\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bh-n:multiparty,<br \/>\r\ntitle = {Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Dang-Trinh Huynh-Ngoc},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf},<br \/>\r\nyear  = {2009},<br \/>\r\ndate = {2009-10-01},<br \/>\r\nurldate = {2009-10-01},<br \/>\r\nbooktitle = {Proceedings 50th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {53\u201362},<br \/>\r\naddress = {Atlanta, GA},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('64','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_64\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('64','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh-Ngoc, Dang-Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('60','tp_links')\" style=\"cursor:pointer;\">On the Value of Multiple Read\/Write Streams for Approximating Frequency Moments<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 49th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 499\u2013508, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Philadelphia, PA, <\/span><span class=\"tp_pub_additional_year\">2008<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_60\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('60','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_60\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bh-n:freq,<br \/>\r\ntitle = {On the Value of Multiple Read\/Write Streams for Approximating Frequency Moments},<br \/>\r\nauthor = {Paul Beame and Dang-Trinh Huynh-Ngoc},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freq.pdf},<br \/>\r\nyear  = {2008},<br \/>\r\ndate = {2008-10-01},<br \/>\r\nbooktitle = {Proceedings 49th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {499\u2013508},<br \/>\r\naddress = {Philadelphia, PA},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('60','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_60\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freq.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freq.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/freq.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('60','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh-Ngoc, Dang-Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('59','tp_links')\" style=\"cursor:pointer;\">On the Value of Multiple Read\/Write Streams for Approximating Frequency Moments<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR08-024, <\/span><span class=\"tp_pub_additional_year\">2008<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_59\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('59','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_59\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bh-n:freq-eccc,<br \/>\r\ntitle = {On the Value of Multiple Read\/Write Streams for Approximating Frequency Moments},<br \/>\r\nauthor = {Paul Beame and Dang-Trinh Huynh-Ngoc},<br \/>\r\nurl = {http:\/\/eccc.hpi-web.de\/eccc-reports\/2008\/TR08-024\/index.html},<br \/>\r\nyear  = {2008},<br \/>\r\ndate = {2008-01-01},<br \/>\r\nnumber = {TR08-024},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('59','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_59\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.hpi-web.de\/eccc-reports\/2008\/TR08-024\/index.html\" title=\"http:\/\/eccc.hpi-web.de\/eccc-reports\/2008\/TR08-024\/index.html\" target=\"_blank\">http:\/\/eccc.hpi-web.de\/eccc-reports\/2008\/TR08-024\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('59','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh-Ngoc, Dang-Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('63','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity and Threshold Circuit Complexity of $AC^0$<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR08-082, <\/span><span class=\"tp_pub_additional_year\">2008<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_63\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('63','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_63\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bh-n:multiparty-eccc,<br \/>\r\ntitle = {Multiparty Communication Complexity and Threshold Circuit Complexity of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Dang-Trinh Huynh-Ngoc},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf},<br \/>\r\nyear  = {2008},<br \/>\r\ndate = {2008-01-01},<br \/>\r\nnumber = {TR08-082},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('63','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_63\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('63','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Jayram, T. S.;  Rudra, Atri<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('130','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Randomized Read\/Write Stream Algorithms<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 689\u2013698, <\/span><span class=\"tp_pub_additional_address\">San Diego, CA, <\/span><span class=\"tp_pub_additional_year\">2007<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_130\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('130','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_130\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bjr:reversal,<br \/>\r\ntitle = {Lower Bounds for Randomized Read\/Write Stream Algorithms},<br \/>\r\nauthor = {Paul Beame and T. S. Jayram and Atri Rudra},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stream.pdf},<br \/>\r\nyear  = {2007},<br \/>\r\ndate = {2007-06-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {689\u2013698},<br \/>\r\naddress = {San Diego, CA},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('130','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_130\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stream.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stream.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stream.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('130','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  David, Matei;  Pitassi, Toniann;  Woelfel, Philipp<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('51','tp_links')\" style=\"cursor:pointer;\">Separating Deterministic from Nondeterministic NOF Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Automata, Languages, and Programming: 34th International Colloquium (ICALP 2007), <\/span><span class=\"tp_pub_additional_pages\">pp. 134\u2013145, <\/span><span class=\"tp_pub_additional_year\">2007<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_51\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('51','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_51\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bdpw:kparty,<br \/>\r\ntitle = {Separating Deterministic from Nondeterministic NOF Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Matei David and Toniann Pitassi and Philipp Woelfel},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icalpkparty.pdf},<br \/>\r\nyear  = {2007},<br \/>\r\ndate = {2007-01-01},<br \/>\r\nbooktitle = {Automata, Languages, and Programming: 34th International Colloquium (ICALP 2007)},<br \/>\r\npages = {134\u2013145},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('51','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_51\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icalpkparty.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icalpkparty.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icalpkparty.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('51','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('128','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 37, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 845\u2013869, <\/span><span class=\"tp_pub_additional_year\">2007<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_128\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('128','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_128\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bps:kfoldtseitin-journal,<br \/>\r\ntitle = {Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf},<br \/>\r\nyear  = {2007},<br \/>\r\ndate = {2007-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {37},<br \/>\r\nnumber = {3},<br \/>\r\npages = {845\u2013869},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('128','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_128\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('128','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan;  Wigderson, Avi<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('125','tp_links')\" style=\"cursor:pointer;\">A Strong Direct Product Theorem for Corruption and the Multiparty Communication Complexity of Set Disjointness<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Computational Complexity, <\/span><span class=\"tp_pub_additional_volume\">vol. 15, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 391\u2013432, <\/span><span class=\"tp_pub_additional_year\">2006<\/span><span class=\"tp_pub_additional_note\">, (Invited submission for special issue on CCC 2005.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_125\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('125','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_125\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bpsw:directsum-journal,<br \/>\r\ntitle = {A Strong Direct Product Theorem for Corruption and the Multiparty Communication Complexity of Set Disjointness},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind and Avi Wigderson},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/directjournal.pdf},<br \/>\r\nyear  = {2006},<br \/>\r\ndate = {2006-01-01},<br \/>\r\njournal = {Computational Complexity},<br \/>\r\nvolume = {15},<br \/>\r\nnumber = {4},<br \/>\r\npages = {391\u2013432},<br \/>\r\nnote = {Invited submission for special issue on CCC 2005.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('125','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_125\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/directjournal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/directjournal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/directjournal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('125','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan;  Wigderson, Avi<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('124','tp_links')\" style=\"cursor:pointer;\">A Direct Sum Theorem for Corruption and the Multiparty NOF Communication Complexity of Set Disjointness<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings Twentieth Annual IEEE Conference on Computational Complexity, <\/span><span class=\"tp_pub_additional_pages\">pp. 52\u201366, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_124\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('124','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_124\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bpsw:directsum,<br \/>\r\ntitle = {A Direct Sum Theorem for Corruption and the Multiparty NOF Communication Complexity of Set Disjointness},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind and Avi Wigderson},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dsum.pdf},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-01-01},<br \/>\r\nbooktitle = {Proceedings Twentieth Annual IEEE Conference on Computational Complexity},<br \/>\r\npages = {52\u201366},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('124','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_124\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dsum.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dsum.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dsum.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('124','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('126','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR05-053, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_126\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('126','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_126\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bps:kfoldtseitin-eccc,<br \/>\r\ntitle = {Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-01-01},<br \/>\r\nnumber = {TR05-053},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('126','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_126\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('126','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('127','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Automata, Languages, and Programming: 32nd International Colloquium (ICALP 2005), <\/span><span class=\"tp_pub_additional_pages\">pp. 1176\u20131188, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_127\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('127','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_127\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bps:kfoldtseitin,<br \/>\r\ntitle = {Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-01-01},<br \/>\r\nbooktitle = {Automata, Languages, and Programming: 32nd International Colloquium (ICALP 2005)},<br \/>\r\npages = {1176\u20131188},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('127','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_127\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('127','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Vee, Erik<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('165','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs, Multiparty Communication \r\n Complexity, and Nearest-Neighbor Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 688-697, <\/span><span class=\"tp_pub_additional_address\">Montreal, Quebec, Canada, <\/span><span class=\"tp_pub_additional_year\">2002<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_165\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('165','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_165\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bv:multibp,<br \/>\r\ntitle = {Time-Space Tradeoffs, Multiparty Communication <br \/>\r\n Complexity, and Nearest-Neighbor Problems},<br \/>\r\nauthor = {Paul Beame and Erik Vee},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf},<br \/>\r\nyear  = {2002},<br \/>\r\ndate = {2002-05-01},<br \/>\r\nurldate = {2002-05-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {688-697},<br \/>\r\naddress = {Montreal, Quebec, Canada},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('165','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_165\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('165','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Tompa, Martin;  Yan, Peiyuan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('143','tp_links')\" style=\"cursor:pointer;\">Communication-Space Tradeoffs for Unrestricted Protocols<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 23, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 652-661, <\/span><span class=\"tp_pub_additional_year\">1994<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_143\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('143','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_143\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bty:communication,<br \/>\r\ntitle = {Communication-Space Tradeoffs for Unrestricted Protocols},<br \/>\r\nauthor = {Paul Beame and Martin Tompa and Peiyuan Yan},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf},<br \/>\r\nyear  = {1994},<br \/>\r\ndate = {1994-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {23},<br \/>\r\nnumber = {3},<br \/>\r\npages = {652-661},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('143','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_143\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/commspace.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('143','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Lawry, Joan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('99','tp_links')\" style=\"cursor:pointer;\">Randomized versus Nondeterministic Communication Complexity<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 188-199, <\/span><span class=\"tp_pub_additional_address\">Victoria, B.C., Canada, <\/span><span class=\"tp_pub_additional_year\">1992<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_99\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('99','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_99\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bl92,<br \/>\r\ntitle = {Randomized versus Nondeterministic Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Joan Lawry},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomvsnondet.pdf},<br \/>\r\nyear  = {1992},<br \/>\r\ndate = {1992-05-01},<br \/>\r\nbooktitle = {Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {188-199},<br \/>\r\naddress = {Victoria, B.C., Canada},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('99','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_99\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomvsnondet.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomvsnondet.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/randomvsnondet.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('99','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-verify\"><strong>Verification of Software and Hardware<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Liew, Vincent;  Beame, Paul;  Devriendt, Jo;  Elfers, Jan;  Nordstr\u00f6m, Jakob<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('188','tp_links')\" style=\"cursor:pointer;\">Verifying Properties of Bit-vector Multiplication Using Cutting Planes Reasoning<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 20th Conference on Formal Methods in Computer Aided Design \u2013 FMCAD 2020, <\/span><span class=\"tp_pub_additional_pages\">pp. 194\u2013204, <\/span><span class=\"tp_pub_additional_publisher\">TU Wein Academic Press, <\/span><span class=\"tp_pub_additional_year\">2020<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_188\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('188','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_188\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{lbden:multiply,<br \/>\r\ntitle = {Verifying Properties of Bit-vector Multiplication Using Cutting Planes Reasoning},<br \/>\r\nauthor = {Vincent Liew and Paul Beame and Jo Devriendt and Jan Elfers and Jakob Nordstr\u00f6m},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf},<br \/>\r\ndoi = {https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6},<br \/>\r\nyear  = {2020},<br \/>\r\ndate = {2020-09-01},<br \/>\r\nbooktitle = {Proceedings of the 20th Conference on Formal Methods in Computer Aided Design \u2013 FMCAD 2020},<br \/>\r\npages = {194\u2013204},<br \/>\r\npublisher = {TU Wein Academic Press},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('188','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_188\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6\" title=\"Follow DOI:https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6\" target=\"_blank\">doi:https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('188','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('109','tp_links')\" style=\"cursor:pointer;\">Toward Verifying Nonlinear Integer Arithmetic<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of the ACM, <\/span><span class=\"tp_pub_additional_volume\">vol. 66, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 22:1-30, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_109\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('109','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_109\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bl:multiply-journal,<br \/>\r\ntitle = {Toward Verifying Nonlinear Integer Arithmetic},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-06-01},<br \/>\r\njournal = {Journal of the ACM},<br \/>\r\nvolume = {66},<br \/>\r\nnumber = {3},<br \/>\r\npages = {22:1-30},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('109','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_109\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('109','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('108','tp_links')\" style=\"cursor:pointer;\">Towards Verifying Nonlinear Integer Arithmetic<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Computer Aided Verification, 29th International Conference, CAV'17 Proceedings, Part II, <\/span><span class=\"tp_pub_additional_pages\">pp. 238\u2013258, <\/span><span class=\"tp_pub_additional_address\">Heidelberg, Germany, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_108\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('108','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_108\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bl:multiply,<br \/>\r\ntitle = {Towards Verifying Nonlinear Integer Arithmetic},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-07-01},<br \/>\r\nbooktitle = {Computer Aided Verification, 29th International Conference, CAV'17 Proceedings, Part II},<br \/>\r\npages = {238\u2013258},<br \/>\r\naddress = {Heidelberg, Germany},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('108','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_108\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('108','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('110','tp_links')\" style=\"cursor:pointer;\">Towards Verifying Nonlinear Integer Arithmetic<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1705.04302, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_110\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('110','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_110\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bl:multiply-tr,<br \/>\r\ntitle = {Towards Verifying Nonlinear Integer Arithmetic},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1705.04302},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-05-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1705.04302},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('110','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_110\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1705.04302\" title=\"http:\/\/arxiv.org\/abs\/1705.04302\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1705.04302<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('110','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Chan, W.;  Anderson, R. J.;  Beame, P.;  Jones, D. J.;  Notkin, D.;  Warner, W. E<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('186','tp_links')\" style=\"cursor:pointer;\">Optimizing Symbolic Model-Checking for Statecharts<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">IEEE Transactions on Software Engineering, <\/span><span class=\"tp_pub_additional_volume\">vol. 27, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 170\u2013190, <\/span><span class=\"tp_pub_additional_year\">2001<\/span><span class=\"tp_pub_additional_note\">, (Special section of invited papers from 21st International \r\n Conference on Software Engineering)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_186\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('186','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_186\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{cabjnw:optimize,<br \/>\r\ntitle = {Optimizing Symbolic Model-Checking for Statecharts},<br \/>\r\nauthor = {W. Chan and R. J. Anderson and P. Beame and D. J. Jones and D. Notkin and W. E Warner},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/tse.pdf},<br \/>\r\nyear  = {2001},<br \/>\r\ndate = {2001-01-01},<br \/>\r\njournal = {IEEE Transactions on Software Engineering},<br \/>\r\nvolume = {27},<br \/>\r\nnumber = {2},<br \/>\r\npages = {170\u2013190},<br \/>\r\nnote = {Special section of invited papers from 21st International <br \/>\r\n Conference on Software Engineering},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('186','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_186\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/tse.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/tse.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/tse.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('186','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Chan, W.;  Anderson, R. J.;  Beame, P.;  Jones, D. J.;  Notkin, D.;  Warner, W. E<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('185','tp_links')\" style=\"cursor:pointer;\">Decoupling Synchronization from Logic for Efficient \r\n Symbolic Model Checking of Statecharts<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 21st International Conference on Software Engineering, <\/span><span class=\"tp_pub_additional_pages\">pp. 142\u2013151, <\/span><span class=\"tp_pub_additional_year\">1999<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_185\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('185','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_185\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{cabjnw:icse99,<br \/>\r\ntitle = {Decoupling Synchronization from Logic for Efficient <br \/>\r\n Symbolic Model Checking of Statecharts},<br \/>\r\nauthor = {W. Chan and R. J. Anderson and P. Beame and D. J. Jones and D. Notkin and W. E Warner},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icse99.pdf},<br \/>\r\nyear  = {1999},<br \/>\r\ndate = {1999-04-01},<br \/>\r\nbooktitle = {Proceedings of the 21st International Conference on Software Engineering},<br \/>\r\npages = {142\u2013151},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('185','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_185\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icse99.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icse99.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/icse99.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('185','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Anderson, Richard J.;  Chan, William;  Beame, Paul;  Notkin, David<\/p><p class=\"tp_pub_title\">Experiences with the Application of Symbolic Model Checking to the \r\n Analysis of Software Specifications <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the \r\n Andrei Ershov Third International Conference on \r\n Perspectives of System Informatics, <\/span><span class=\"tp_pub_additional_pages\">pp. 355-361, <\/span><span class=\"tp_pub_additional_address\">Novosibirsk, Russia, <\/span><span class=\"tp_pub_additional_year\">1999<\/span>.<\/p><p class=\"tp_pub_menu\"><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_10\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{acbn:siberia,<br \/>\r\ntitle = {Experiences with the Application of Symbolic Model Checking to the <br \/>\r\n Analysis of Software Specifications},<br \/>\r\nauthor = {Richard J. Anderson and William Chan and Paul Beame and David Notkin},<br \/>\r\nyear  = {1999},<br \/>\r\ndate = {1999-01-01},<br \/>\r\nbooktitle = {Proceedings of the <br \/>\r\n Andrei Ershov Third International Conference on <br \/>\r\n Perspectives of System Informatics},<br \/>\r\npages = {355-361},<br \/>\r\naddress = {Novosibirsk, Russia},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('10','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Chan, W.;  Anderson, R. J.;  Beame, P.;  Burns, S.;  Modugno, F.;  Notkin, D.;  Reese, J. D.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('181','tp_links')\" style=\"cursor:pointer;\">Model Checking Large Software Specifications<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">IEEE Transactions on Software Engineering, <\/span><span class=\"tp_pub_additional_volume\">vol. 24, <\/span><span class=\"tp_pub_additional_number\">no. 7, <\/span><span class=\"tp_pub_additional_pages\">pp. 498\u2013520, <\/span><span class=\"tp_pub_additional_year\">1998<\/span><span class=\"tp_pub_additional_note\">, (Special section of invited papers from 4th Foundations in \r\n Software Engineering Conference)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_181\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('181','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_181\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{cabbnmnr:tse,<br \/>\r\ntitle = {Model Checking Large Software Specifications},<br \/>\r\nauthor = {W. Chan and R. J. Anderson and P. Beame and S. Burns and F. Modugno and D. Notkin and J. D. Reese},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/modelchecklarge.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-07-01},<br \/>\r\njournal = {IEEE Transactions on Software Engineering},<br \/>\r\nvolume = {24},<br \/>\r\nnumber = {7},<br \/>\r\npages = {498\u2013520},<br \/>\r\nnote = {Special section of invited papers from 4th Foundations in <br \/>\r\n Software Engineering Conference},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('181','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_181\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/modelchecklarge.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/modelchecklarge.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/modelchecklarge.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('181','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Chan, W.;  Anderson, R. J.;  Beame, P.;  Notkin, D.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('183','tp_links')\" style=\"cursor:pointer;\">Improving Efficiency of Symbolic Model Checking for \r\n State-Based System Requirements<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Young, M. (Ed.): <span class=\"tp_pub_additional_booktitle\">ISSTA 98: Proceedings of the ACM SIGSOFT International Symposium on Software Testing and Analysis, <\/span><span class=\"tp_pub_additional_pages\">pp. 102\u2013112, <\/span><span class=\"tp_pub_additional_address\">Clearwater Beach, FL, <\/span><span class=\"tp_pub_additional_year\">1998<\/span><span class=\"tp_pub_additional_note\">, (Published as textitSoftware Engineering Notes, 23(2), March1998)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_183\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('183','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_183\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{cabn:issta98,<br \/>\r\ntitle = {Improving Efficiency of Symbolic Model Checking for <br \/>\r\n State-Based System Requirements},<br \/>\r\nauthor = {W. Chan and R. J. Anderson and P. Beame and D. Notkin},<br \/>\r\neditor = {M. Young},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/issta98.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-03-01},<br \/>\r\nbooktitle = {ISSTA 98: Proceedings of the ACM SIGSOFT International Symposium on Software Testing and Analysis},<br \/>\r\npages = {102\u2013112},<br \/>\r\naddress = {Clearwater Beach, FL},<br \/>\r\ncrossref = {issta98},<br \/>\r\nnote = {Published as textitSoftware Engineering Notes, 23(2), March1998},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('183','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_183\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/issta98.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/issta98.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/issta98.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('183','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Chan, W.;  Anderson, R. J.;  Beame, P.;  Notkin, D.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('182','tp_links')\" style=\"cursor:pointer;\">Combining Constraint Solving and Symbolic Model Checking \r\n for a Class of Systems with Non-Linear Constraints<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Grumberg, O. (Ed.): <span class=\"tp_pub_additional_booktitle\">Computer Aided Verification, 9th International Conference, CAV'97 Proceedings, <\/span><span class=\"tp_pub_additional_pages\">pp. 316\u2013327, <\/span><span class=\"tp_pub_additional_publisher\">Springer-Verlag, <\/span><span class=\"tp_pub_additional_address\">Haifa, Israel, <\/span><span class=\"tp_pub_additional_year\">1997<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_182\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('182','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_182\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{cabn:cav97,<br \/>\r\ntitle = {Combining Constraint Solving and Symbolic Model Checking <br \/>\r\n for a Class of Systems with Non-Linear Constraints},<br \/>\r\nauthor = {W. Chan and R. J. Anderson and P. Beame and D. Notkin},<br \/>\r\neditor = {O. Grumberg},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cav97.pdf},<br \/>\r\nyear  = {1997},<br \/>\r\ndate = {1997-06-01},<br \/>\r\nbooktitle = {Computer Aided Verification, 9th International Conference, CAV'97 Proceedings},<br \/>\r\nvolume = {1254},<br \/>\r\npages = {316\u2013327},<br \/>\r\npublisher = {Springer-Verlag},<br \/>\r\naddress = {Haifa, Israel},<br \/>\r\nseries = {Lecture Notes in Computer Science},<br \/>\r\ncrossref = {cav97},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('182','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_182\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cav97.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cav97.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cav97.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('182','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Anderson, R. J.;  Beame, P.;  Burns, S.;  Chan, W.;  Modugno, F.;  Notkin, D.;  Reese, J. D.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('179','tp_links')\" style=\"cursor:pointer;\">Model Checking Large Software Specifications<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Garlan, D. (Ed.): <span class=\"tp_pub_additional_booktitle\">Proceedings of the 4th ACM SIGSOFT Symposium on the Foundations of Software Engineering, <\/span><span class=\"tp_pub_additional_pages\">pp. 156\u2013166, <\/span><span class=\"tp_pub_additional_address\">San Francisco, CA, <\/span><span class=\"tp_pub_additional_year\">1996<\/span><span class=\"tp_pub_additional_note\">, (Also published as textitSoftware Engineering Notes, 21(6), November 1996)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_179\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('179','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_179\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{abbcmnr:fse,<br \/>\r\ntitle = {Model Checking Large Software Specifications},<br \/>\r\nauthor = {R. J. Anderson and P. Beame and S. Burns and W. Chan and F. Modugno and D. Notkin and J. D. Reese},<br \/>\r\neditor = {D. Garlan},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/fse.pdf},<br \/>\r\nyear  = {1996},<br \/>\r\ndate = {1996-10-01},<br \/>\r\nurldate = {1996-10-01},<br \/>\r\nbooktitle = {Proceedings of the 4th ACM SIGSOFT Symposium on the Foundations of Software Engineering},<br \/>\r\npages = {156\u2013166},<br \/>\r\naddress = {San Francisco, CA},<br \/>\r\ncrossref = {fse96},<br \/>\r\nnote = {Also published as textitSoftware Engineering Notes, 21(6), November 1996},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('179','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_179\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/fse.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/fse.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/fse.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('179','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-proofsat\"><strong>Proof Complexity and Satisfiability<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('293','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR25-057, <\/span><span class=\"tp_pub_additional_year\">2025<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_293\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('293','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_293\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bw:multiparty-collision-eccc,<br \/>\r\ntitle = {Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles},<br \/>\r\nauthor = {Paul Beame and Michael Whitmeyer},<br \/>\r\nurl = {https:\/\/eccc.weizmann.ac.il\/report\/2025\/057},<br \/>\r\nyear  = {2025},<br \/>\r\ndate = {2025-01-01},<br \/>\r\nnumber = {TR25-057},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('293','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_293\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/eccc.weizmann.ac.il\/report\/2025\/057\" title=\"https:\/\/eccc.weizmann.ac.il\/report\/2025\/057\" target=\"_blank\">https:\/\/eccc.weizmann.ac.il\/report\/2025\/057<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('293','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('294','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Automata, Languages, and Programming: 52nd International Colloquium (ICALP 2025), <\/span><span class=\"tp_pub_additional_pages\">pp. 21:1\u201321:20, <\/span><span class=\"tp_pub_additional_year\">2025<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_294\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('294','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_294\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bw:multiparty-collision,<br \/>\r\ntitle = {Multiparty Communication Complexity of Collision-Finding and Cutting Planes Proofs of Concise Pigeonhole Principles},<br \/>\r\nauthor = {Paul Beame and Michael Whitmeyer},<br \/>\r\nurl = {https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf},<br \/>\r\ndoi = {10.4230\/LIPICS.ICALP.2025.21},<br \/>\r\nyear  = {2025},<br \/>\r\ndate = {2025-01-01},<br \/>\r\nurldate = {2025-01-01},<br \/>\r\nbooktitle = {Automata, Languages, and Programming: 52nd International Colloquium (ICALP 2025)},<br \/>\r\nvolume = {334},<br \/>\r\npages = {21:1\u201321:20},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('294','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_294\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf\" title=\"https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf\" target=\"_blank\">https:\/\/www.cs.washington.edu\/homes\/beame\/papers\/Collision.ICALP.2025.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.4230\/LIPICS.ICALP.2025.21\" title=\"Follow DOI:10.4230\/LIPICS.ICALP.2025.21\" target=\"_blank\">doi:10.4230\/LIPICS.ICALP.2025.21<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('294','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Whitmeyer, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('292','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity of Collision-Finding<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">arxiv\/math.co <\/span><span class=\"tp_pub_additional_number\">no. arXiv:2411.07400, <\/span><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_292\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('292','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_292\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bw:multiparty-collision-arxiv,<br \/>\r\ntitle = {Multiparty Communication Complexity of Collision-Finding},<br \/>\r\nauthor = {Paul Beame and Michael Whitmeyer},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/2411.07400},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-01-01},<br \/>\r\nnumber = {arXiv:2411.07400},<br \/>\r\ninstitution = {arxiv\/math.co},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('292','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_292\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/2411.07400\" title=\"http:\/\/arxiv.org\/abs\/2411.07400\" target=\"_blank\">http:\/\/arxiv.org\/abs\/2411.07400<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('292','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koroth, Sajin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('87','tp_links')\" style=\"cursor:pointer;\">On Disperser\/Lifting Properties of the Index and Inner-Product Functions<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">14th Innovations in Theoretical Computer Science Conference, ITCS \r\n 2023, January 10\u201313, 2023, Cambridge, MA, USA, <\/span><span class=\"tp_pub_additional_pages\">pp. 14:1-14:17, <\/span><span class=\"tp_pub_additional_publisher\">Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_87\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('87','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_87\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bk:lift-itcs,<br \/>\r\ntitle = {On Disperser\/Lifting Properties of the Index and Inner-Product Functions},<br \/>\r\nauthor = {Paul Beame and Sajin Koroth},<br \/>\r\ndoi = {https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-01-01},<br \/>\r\nbooktitle = {14th Innovations in Theoretical Computer Science Conference, ITCS <br \/>\r\n 2023, January 10\u201313, 2023, Cambridge, MA, USA},<br \/>\r\nvolume = {251},<br \/>\r\npages = {14:1-14:17},<br \/>\r\npublisher = {Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik},<br \/>\r\nseries = {LIPIcs},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('87','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_87\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14\" title=\"Follow DOI:https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14\" target=\"_blank\">doi:https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2023.14<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('87','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koroth, Sajin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('86','tp_links')\" style=\"cursor:pointer;\">On Disperser\/Lifting Properties of the Index and Inner-Product Functions<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/2211.17211, <\/span><span class=\"tp_pub_additional_year\">2022<\/span><span class=\"tp_pub_additional_note\">, (ECCC Technical Report TR22-173 http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_86\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('86','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_86\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bk:lift-tr,<br \/>\r\ntitle = {On Disperser\/Lifting Properties of the Index and Inner-Product Functions},<br \/>\r\nauthor = {Paul Beame and Sajin Koroth},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/2211.17211 <br \/>\r\nhttp:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html},<br \/>\r\nyear  = {2022},<br \/>\r\ndate = {2022-01-01},<br \/>\r\nurldate = {2022-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/2211.17211},<br \/>\r\nnote = {ECCC Technical Report TR22-173 http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('86','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_86\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/2211.17211\" title=\"http:\/\/arxiv.org\/abs\/2211.17211\" target=\"_blank\">http:\/\/arxiv.org\/abs\/2211.17211<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html\" title=\"http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html\" target=\"_blank\">http:\/\/eccc.weizmann.ac.il\/report\/2022\/173\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('86','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Kaufmann, Daniela;  Beame, Paul;  Biere, Armin;  Nordstr\u00f6m, Jakob<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('173','tp_links')\" style=\"cursor:pointer;\">Adding Dual Variables to Algebraic Reasoning for Circuit Verification<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of 25th Design, Automation and Test in Europe (DATE), <\/span><span class=\"tp_pub_additional_pages\">pp. 1435\u20131440, <\/span><span class=\"tp_pub_additional_publisher\">IEEE, <\/span><span class=\"tp_pub_additional_year\">2022<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_173\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('173','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_173\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{kbbn:dual,<br \/>\r\ntitle = {Adding Dual Variables to Algebraic Reasoning for Circuit Verification},<br \/>\r\nauthor = {Daniela Kaufmann and Paul Beame and Armin Biere and Jakob Nordstr\u00f6m},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dual-verify.pdf},<br \/>\r\nyear  = {2022},<br \/>\r\ndate = {2022-01-01},<br \/>\r\nbooktitle = {Proceedings of 25th Design, Automation and Test in Europe (DATE)},<br \/>\r\npages = {1435\u20131440},<br \/>\r\npublisher = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('173','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_173\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dual-verify.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dual-verify.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/dual-verify.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('173','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Liew, Vincent;  Beame, Paul;  Devriendt, Jo;  Elfers, Jan;  Nordstr\u00f6m, Jakob<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('188','tp_links')\" style=\"cursor:pointer;\">Verifying Properties of Bit-vector Multiplication Using Cutting Planes Reasoning<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 20th Conference on Formal Methods in Computer Aided Design \u2013 FMCAD 2020, <\/span><span class=\"tp_pub_additional_pages\">pp. 194\u2013204, <\/span><span class=\"tp_pub_additional_publisher\">TU Wein Academic Press, <\/span><span class=\"tp_pub_additional_year\">2020<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_188\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('188','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_188\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{lbden:multiply,<br \/>\r\ntitle = {Verifying Properties of Bit-vector Multiplication Using Cutting Planes Reasoning},<br \/>\r\nauthor = {Vincent Liew and Paul Beame and Jo Devriendt and Jan Elfers and Jakob Nordstr\u00f6m},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf},<br \/>\r\ndoi = {https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6},<br \/>\r\nyear  = {2020},<br \/>\r\ndate = {2020-09-01},<br \/>\r\nbooktitle = {Proceedings of the 20th Conference on Formal Methods in Computer Aided Design \u2013 FMCAD 2020},<br \/>\r\npages = {194\u2013204},<br \/>\r\npublisher = {TU Wein Academic Press},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('188','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_188\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nonlinear-cutting-planes.pdf<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6\" title=\"Follow DOI:https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6\" target=\"_blank\">doi:https:\/\/doi.org\/10.34727\/2020\/isbn.978-3-85448-042-6<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('188','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('109','tp_links')\" style=\"cursor:pointer;\">Toward Verifying Nonlinear Integer Arithmetic<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of the ACM, <\/span><span class=\"tp_pub_additional_volume\">vol. 66, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 22:1-30, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_109\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('109','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_109\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bl:multiply-journal,<br \/>\r\ntitle = {Toward Verifying Nonlinear Integer Arithmetic},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-06-01},<br \/>\r\njournal = {Journal of the ACM},<br \/>\r\nvolume = {66},<br \/>\r\nnumber = {3},<br \/>\r\npages = {22:1-30},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('109','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_109\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('109','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Shih, Andy; den Broeck, Guy Van;  Beame, Paul;  Amarilli, Antoine<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('131','tp_links')\" style=\"cursor:pointer;\">Smoothing Structured Decomposable Circuits<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1906.00311, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_131\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('131','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_131\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{svba:smooth-tr,<br \/>\r\ntitle = {Smoothing Structured Decomposable Circuits},<br \/>\r\nauthor = {Andy Shih and Guy Van den Broeck and Paul Beame and Antoine Amarilli},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1906.00311},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\nurldate = {2019-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1906.00311},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('131','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_131\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1906.00311\" title=\"http:\/\/arxiv.org\/abs\/1906.00311\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1906.00311<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('131','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Shih, Andy; den Broeck, Guy Van;  Beame, Paul;  Amarilli, Antoine<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('132','tp_links')\" style=\"cursor:pointer;\">Smoothing Structured Decomposable Circuits<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Advances in Neural Information Processing Systems 32: Annual Conference \r\n on Neural Information Processing Systems 2019, NeurIPS 2019, <\/span><span class=\"tp_pub_additional_pages\">pp. 11412\u201311422, <\/span><span class=\"tp_pub_additional_year\">2019<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_132\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('132','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_132\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{svba:smooth,<br \/>\r\ntitle = {Smoothing Structured Decomposable Circuits},<br \/>\r\nauthor = {Andy Shih and Guy Van den Broeck and Paul Beame and Antoine Amarilli},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/smoothing-decomposable-circuits.pdf},<br \/>\r\nyear  = {2019},<br \/>\r\ndate = {2019-01-01},<br \/>\r\nbooktitle = {Advances in Neural Information Processing Systems 32: Annual Conference <br \/>\r\n on Neural Information Processing Systems 2019, NeurIPS 2019},<br \/>\r\npages = {11412\u201311422},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('132','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_132\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/smoothing-decomposable-circuits.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/smoothing-decomposable-circuits.[...]\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/smoothing-decomposable-circuits.[...]<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('132','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Fleming, Noah;  Impagliazzo, Russell;  Kolokolova, Antonina;  Pankratov, Denis;  Pitassi, Toniann;  Robere, Robert<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('149','tp_links')\" style=\"cursor:pointer;\">Stabbing Planes<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 9th Innovations in Theoretical \r\n Computer Science Conference (ITCS 2018), <\/span><span class=\"tp_pub_additional_pages\">pp. 10:1\u201310:20, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_149\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('149','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_149\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bfikppr:stabbing,<br \/>\r\ntitle = {Stabbing Planes},<br \/>\r\nauthor = {Paul Beame and Noah Fleming and Russell Impagliazzo and Antonina Kolokolova and Denis Pankratov and Toniann Pitassi and Robert Robere},<br \/>\r\nurl = {http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8341},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-01-01},<br \/>\r\nbooktitle = {Proceedings of the 9th Innovations in Theoretical <br \/>\r\n Computer Science Conference (ITCS 2018)},<br \/>\r\nvolume = {94},<br \/>\r\npages = {10:1\u201310:20},<br \/>\r\nseries = {Leibniz International Proceedings in Informatics (LIPIcs)},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('149','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_149\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8341\" title=\"http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8341\" target=\"_blank\">http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8341<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('149','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('108','tp_links')\" style=\"cursor:pointer;\">Towards Verifying Nonlinear Integer Arithmetic<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Computer Aided Verification, 29th International Conference, CAV'17 Proceedings, Part II, <\/span><span class=\"tp_pub_additional_pages\">pp. 238\u2013258, <\/span><span class=\"tp_pub_additional_address\">Heidelberg, Germany, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_108\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('108','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_108\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bl:multiply,<br \/>\r\ntitle = {Towards Verifying Nonlinear Integer Arithmetic},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-07-01},<br \/>\r\nbooktitle = {Computer Aided Verification, 29th International Conference, CAV'17 Proceedings, Part II},<br \/>\r\npages = {238\u2013258},<br \/>\r\naddress = {Heidelberg, Germany},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('108','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_108\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiply.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('108','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('110','tp_links')\" style=\"cursor:pointer;\">Towards Verifying Nonlinear Integer Arithmetic<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1705.04302, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_110\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('110','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_110\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bl:multiply-tr,<br \/>\r\ntitle = {Towards Verifying Nonlinear Integer Arithmetic},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1705.04302},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-05-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1705.04302},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('110','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_110\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1705.04302\" title=\"http:\/\/arxiv.org\/abs\/1705.04302\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1705.04302<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('110','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Li, Jerry;  Roy, Sudeepa;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('103','tp_links')\" style=\"cursor:pointer;\">Exact Model Counting of Query Expressions: Limitations of Propositional Methods<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">ACM Transactions on Database Systems, <\/span><span class=\"tp_pub_additional_volume\">vol. 42, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 1:1\u201345, <\/span><span class=\"tp_pub_additional_year\">2017<\/span><span class=\"tp_pub_additional_note\">, (Invited paper from 2014 International Conference on Database Theory (ICDT) combined with preliminary version in Proceedings of the 2013 Conference on \r\n Uncertainty in Artificial Intelligence (UAI).)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_103\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('103','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_103\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{blrs:numsat-journal,<br \/>\r\ntitle = {Exact Model Counting of Query Expressions: Limitations of Propositional Methods},<br \/>\r\nauthor = {Paul Beame and Jerry Li and Sudeepa Roy and Dan Suciu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/numsat-journal.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-03-01},<br \/>\r\njournal = {ACM Transactions on Database Systems},<br \/>\r\nvolume = {42},<br \/>\r\nnumber = {1},<br \/>\r\npages = {1:1\u201345},<br \/>\r\nnote = {Invited paper from 2014 International Conference on Database Theory (ICDT) combined with preliminary version in Proceedings of the 2013 Conference on <br \/>\r\n Uncertainty in Artificial Intelligence (UAI).},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('103','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_103\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/numsat-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/numsat-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/numsat-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('103','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Fleming, Noah;  Impagliazzo, Russell;  Kolokolova, Antonina;  Pankratov, Denis;  Pitassi, Toniann;  Robere, Robert<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('148','tp_links')\" style=\"cursor:pointer;\">Stabbing Planes<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1710.03219, <\/span><span class=\"tp_pub_additional_year\">2017<\/span><span class=\"tp_pub_additional_note\">, (Also Technical Report TR17-151 Electronic Colloquium on Computational Complexity available at http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/151\/index.html)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_148\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('148','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_148\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bfikppr:stabbing-tr,<br \/>\r\ntitle = {Stabbing Planes},<br \/>\r\nauthor = {Paul Beame and Noah Fleming and Russell Impagliazzo and Antonina Kolokolova and Denis Pankratov and Toniann Pitassi and Robert Robere},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1710.03219 <br \/>\r\nhttp:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/151\/index.html},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\nurldate = {2017-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1710.03219},<br \/>\r\nnote = {Also Technical Report TR17-151 Electronic Colloquium on Computational Complexity available at http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/151\/index.html},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('148','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_148\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1710.03219\" title=\"http:\/\/arxiv.org\/abs\/1710.03219\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1710.03219<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/151\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/151\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2017\/151\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('148','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Beck, Chris;  Impagliazzo, Russell<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('26','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for \r\n Superlinear Space<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 45, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 1612\u20131645, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_26\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('26','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_26\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbi:proofspace-journal,<br \/>\r\ntitle = {Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for <br \/>\r\n Superlinear Space},<br \/>\r\nauthor = {Paul Beame and Chris Beck and Russell Impagliazzo},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {45},<br \/>\r\nnumber = {4},<br \/>\r\npages = {1612\u20131645},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('26','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_26\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('26','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('105','tp_links')\" style=\"cursor:pointer;\">New Limits for Knowledge Compilation and Applications to Exact Model Counting<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 31st  Conference on Uncertainty in Artificial Intelligence, <\/span><span class=\"tp_pub_additional_pages\">pp. 131\u2013140, <\/span><span class=\"tp_pub_additional_address\">Amsterdam, <\/span><span class=\"tp_pub_additional_year\">2015<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_105\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('105','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_105\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bl:sdd,<br \/>\r\ntitle = {New Limits for Knowledge Compilation and Applications to Exact Model Counting},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sdd.pdf},<br \/>\r\nyear  = {2015},<br \/>\r\ndate = {2015-07-01},<br \/>\r\nbooktitle = {Proceedings 31st  Conference on Uncertainty in Artificial Intelligence},<br \/>\r\npages = {131\u2013140},<br \/>\r\naddress = {Amsterdam},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('105','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_105\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sdd.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sdd.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/sdd.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('105','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Broeck, Guy Van;  Gribkoff, Eric;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('39','tp_links')\" style=\"cursor:pointer;\">Symmetric Weighted First-Order Model Counting<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Fourth Annual ACM Symposium on Principles of Database Systems, <\/span><span class=\"tp_pub_additional_pages\">pp. 313\u2013328, <\/span><span class=\"tp_pub_additional_year\">2015<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_39\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('39','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_39\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bbgs:symm-pods,<br \/>\r\ntitle = {Symmetric Weighted First-Order Model Counting},<br \/>\r\nauthor = {Paul Beame and Guy Van Broeck and Eric Gribkoff and Dan Suciu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm-count-pods.pdf},<br \/>\r\nyear  = {2015},<br \/>\r\ndate = {2015-06-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Fourth Annual ACM Symposium on Principles of Database Systems},<br \/>\r\npages = {313\u2013328},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('39','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_39\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm-count-pods.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm-count-pods.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm-count-pods.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('39','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Liew, Vincent<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('104','tp_links')\" style=\"cursor:pointer;\">New Limits for Knowledge Compilation and Applications to Exact Model Counting<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1506.02639, <\/span><span class=\"tp_pub_additional_year\">2015<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_104\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('104','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_104\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bl:sdd-tr,<br \/>\r\ntitle = {New Limits for Knowledge Compilation and Applications to Exact Model Counting},<br \/>\r\nauthor = {Paul Beame and Vincent Liew},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1506.02639},<br \/>\r\nyear  = {2015},<br \/>\r\ndate = {2015-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1506.02639},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('104','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_104\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1506.02639\" title=\"http:\/\/arxiv.org\/abs\/1506.02639\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1506.02639<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('104','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('133','tp_links')\" style=\"cursor:pointer;\">Non-Restarting SAT Solvers with Simple Preprocessing Can Efficiently Simulate Resolution<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings, AAAI-14: Twenty-Eighth National Conference on Artificial Intelligence, <\/span><span class=\"tp_pub_additional_pages\">pp. 2608\u20132615, <\/span><span class=\"tp_pub_additional_organization\">American Association for Artificial Intelligence <\/span><span class=\"tp_pub_additional_address\">Quebec City, Canada, <\/span><span class=\"tp_pub_additional_year\">2014<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_133\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('133','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_133\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bs:cdcl,<br \/>\r\ntitle = {Non-Restarting SAT Solvers with Simple Preprocessing Can Efficiently Simulate Resolution},<br \/>\r\nauthor = {Paul Beame and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cdclres.pdf},<br \/>\r\nyear  = {2014},<br \/>\r\ndate = {2014-07-01},<br \/>\r\nurldate = {2014-01-01},<br \/>\r\nbooktitle = {Proceedings, AAAI-14: Twenty-Eighth National Conference on Artificial Intelligence},<br \/>\r\npages = {2608\u20132615},<br \/>\r\naddress = {Quebec City, Canada},<br \/>\r\norganization = {American Association for Artificial Intelligence},<br \/>\r\ncrossref = {aaai14},<br \/>\r\nkey = {AAAI-14},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('133','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_133\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cdclres.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cdclres.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cdclres.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('133','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Li, Jerry;  Roy, Sudeepa;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('101','tp_links')\" style=\"cursor:pointer;\">Model Counting of Query Expressions: Limitations of Propositional Methods<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of 17th International Conference on Database Theory, <\/span><span class=\"tp_pub_additional_pages\">pp. 177\u2013188, <\/span><span class=\"tp_pub_additional_year\">2014<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_101\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('101','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_101\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{blrs:dldd-icdt,<br \/>\r\ntitle = {Model Counting of Query Expressions: Limitations of Propositional Methods},<br \/>\r\nauthor = {Paul Beame and Jerry Li and Sudeepa Roy and Dan Suciu},<br \/>\r\nurl = {http:\/\/dx.doi.org\/10.5441\/002\/icdt.2014.20},<br \/>\r\nyear  = {2014},<br \/>\r\ndate = {2014-03-01},<br \/>\r\nbooktitle = {Proceedings of 17th International Conference on Database Theory},<br \/>\r\npages = {177\u2013188},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('101','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_101\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/dx.doi.org\/10.5441\/002\/icdt.2014.20\" title=\"http:\/\/dx.doi.org\/10.5441\/002\/icdt.2014.20\" target=\"_blank\">http:\/\/dx.doi.org\/10.5441\/002\/icdt.2014.20<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('101','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Broeck, Guy Van;  Gribkoff, Eric;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('38','tp_links')\" style=\"cursor:pointer;\">Symmetric Weighted First-Order Model Counting<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1506.02639, <\/span><span class=\"tp_pub_additional_year\">2014<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_38\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('38','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_38\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbgs:symm-tr,<br \/>\r\ntitle = {Symmetric Weighted First-Order Model Counting},<br \/>\r\nauthor = {Paul Beame and Guy Van Broeck and Eric Gribkoff and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1412.1505},<br \/>\r\nyear  = {2014},<br \/>\r\ndate = {2014-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1506.02639},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('38','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_38\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1412.1505\" title=\"http:\/\/arxiv.org\/abs\/1412.1505\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1412.1505<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('38','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Li, Jerry;  Roy, Sudeepa;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('100','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Exact Model Counting and Applications in Probabilistic Databases<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 29th  Conference on Uncertainty in Artificial Intelligence, <\/span><span class=\"tp_pub_additional_pages\">pp. 52\u201361, <\/span><span class=\"tp_pub_additional_address\">Bellevue, WA, <\/span><span class=\"tp_pub_additional_year\">2013<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_100\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('100','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_100\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{blrs:dnnf-uai,<br \/>\r\ntitle = {Lower Bounds for Exact Model Counting and Applications in Probabilistic Databases},<br \/>\r\nauthor = {Paul Beame and Jerry Li and Sudeepa Roy and Dan Suciu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/uai13.pdf},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-07-01},<br \/>\r\nbooktitle = {Proceedings 29th  Conference on Uncertainty in Artificial Intelligence},<br \/>\r\npages = {52\u201361},<br \/>\r\naddress = {Bellevue, WA},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('100','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_100\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/uai13.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/uai13.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/uai13.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('100','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Li, Jerry;  Roy, Sudeepa;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('102','tp_links')\" style=\"cursor:pointer;\">Model Counting of Query Expressions: Limitations of Propositional Methods<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1312.4125, <\/span><span class=\"tp_pub_additional_year\">2013<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_102\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('102','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_102\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{blrs:dldd-arxiv,<br \/>\r\ntitle = {Model Counting of Query Expressions: Limitations of Propositional Methods},<br \/>\r\nauthor = {Paul Beame and Jerry Li and Sudeepa Roy and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1312.4125},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1312.4125},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('102','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_102\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1312.4125\" title=\"http:\/\/arxiv.org\/abs\/1312.4125\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1312.4125<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('102','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Beck, Chris;  Impagliazzo, Russell<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('25','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for \r\n Superlinear Space<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 212\u2013232, <\/span><span class=\"tp_pub_additional_address\">New York, NY, <\/span><span class=\"tp_pub_additional_year\">2012<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_25\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('25','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_25\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bbi:proofspace,<br \/>\r\ntitle = {Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for <br \/>\r\n Superlinear Space},<br \/>\r\nauthor = {Paul Beame and Chris Beck and Russell Impagliazzo},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-05-01},<br \/>\r\nbooktitle = {Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {212\u2013232},<br \/>\r\naddress = {New York, NY},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('25','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_25\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspace.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('25','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Beck, Chris;  Impagliazzo, Russell<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('24','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for \r\n Superlinear Space<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR11-149, <\/span><span class=\"tp_pub_additional_year\">2011<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_24\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('24','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_24\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bbi:proofspace-eccc,<br \/>\r\ntitle = {Time-Space Tradeoffs in Resolution: Superpolynomial Lower Bounds for <br \/>\r\n Superlinear Space},<br \/>\r\nauthor = {Paul Beame and Chris Beck and Russell Impagliazzo},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf},<br \/>\r\nyear  = {2011},<br \/>\r\ndate = {2011-11-01},<br \/>\r\nnumber = {TR11-149},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('24','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_24\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofspaceeccc.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('24','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('75','tp_links')\" style=\"cursor:pointer;\">Formula Caching in DPLL<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">ACM Transactions on Computation Theory, <\/span><span class=\"tp_pub_additional_volume\">vol. 1, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 9:1-33, <\/span><span class=\"tp_pub_additional_year\">2010<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_75\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('75','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_75\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bips:caching-journal,<br \/>\r\ntitle = {Formula Caching in DPLL},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching-journal.pdf},<br \/>\r\nyear  = {2010},<br \/>\r\ndate = {2010-03-01},<br \/>\r\njournal = {ACM Transactions on Computation Theory},<br \/>\r\nvolume = {1},<br \/>\r\nnumber = {3},<br \/>\r\npages = {9:1-33},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('75','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_75\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('75','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('77','tp_links')\" style=\"cursor:pointer;\">The Resolution Complexity of Independent Sets and Vertex Covers in \r\n Random Graphs<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Computational Complexity, <\/span><span class=\"tp_pub_additional_volume\">vol. 16, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 245\u2013297, <\/span><span class=\"tp_pub_additional_year\">2007<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_77\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('77','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_77\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bis:independent-journal,<br \/>\r\ntitle = {The Resolution Complexity of Independent Sets and Vertex Covers in <br \/>\r\n Random Graphs},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/indset.pdf},<br \/>\r\nyear  = {2007},<br \/>\r\ndate = {2007-01-01},<br \/>\r\njournal = {Computational Complexity},<br \/>\r\nvolume = {16},<br \/>\r\nnumber = {3},<br \/>\r\npages = {245\u2013297},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('77','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_77\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/indset.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/indset.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/indset.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('77','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('128','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 37, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 845\u2013869, <\/span><span class=\"tp_pub_additional_year\">2007<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_128\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('128','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_128\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bps:kfoldtseitin-journal,<br \/>\r\ntitle = {Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf},<br \/>\r\nyear  = {2007},<br \/>\r\ndate = {2007-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {37},<br \/>\r\nnumber = {3},<br \/>\r\npages = {845\u2013869},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('128','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_128\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('128','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Sang, Tian;  Beame, Paul;  Kautz, Henry<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('178','tp_links')\" style=\"cursor:pointer;\">A dynamic approach for MPE and Weighted MAX-SAT<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 20th International Joint Conference in \r\n Artificial Intelligence (IJCAI), <\/span><span class=\"tp_pub_additional_pages\">pp. 173\u2013179, <\/span><span class=\"tp_pub_additional_address\">Hyderabad, India, <\/span><span class=\"tp_pub_additional_year\">2007<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_178\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('178','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_178\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{sbk:mpe,<br \/>\r\ntitle = {A dynamic approach for MPE and Weighted MAX-SAT},<br \/>\r\nauthor = {Tian Sang and Paul Beame and Henry Kautz},<br \/>\r\ndoi = {10.5555\/1625275.1625302},<br \/>\r\nyear  = {2007},<br \/>\r\ndate = {2007-01-01},<br \/>\r\nurldate = {2007-01-01},<br \/>\r\nbooktitle = {Proceedings of the 20th International Joint Conference in <br \/>\r\n Artificial Intelligence (IJCAI)},<br \/>\r\npages = {173\u2013179},<br \/>\r\naddress = {Hyderabad, India},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('178','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_178\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.5555\/1625275.1625302\" title=\"Follow DOI:10.5555\/1625275.1625302\" target=\"_blank\">doi:10.5555\/1625275.1625302<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('178','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('74','tp_links')\" style=\"cursor:pointer;\">Formula Caching in DPLL<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR06-140, <\/span><span class=\"tp_pub_additional_year\">2006<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_74\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('74','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_74\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bips:caching-eccc,<br \/>\r\ntitle = {Formula Caching in DPLL},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/eccc.uni-trier.de\/eccc-reports\/2006\/TR06-140\/index.html},<br \/>\r\nyear  = {2006},<br \/>\r\ndate = {2006-01-01},<br \/>\r\nnumber = {TR06-140},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('74','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_74\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2006\/TR06-140\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2006\/TR06-140\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2006\/TR06-140\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('74','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Sang, Tian;  Beame, Paul;  Kautz, Henry<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('176','tp_links')\" style=\"cursor:pointer;\">Performing Bayesian Inference by Weighted Model Counting.<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings, AAAI-05: Twentieth National Conference on Artificial Intelligence, <\/span><span class=\"tp_pub_additional_pages\">pp. 475-482, <\/span><span class=\"tp_pub_additional_organization\">American Association for Artificial Intelligence <\/span><span class=\"tp_pub_additional_address\">Pittsburgh, PA, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_176\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('176','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_176\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{sbk:bayes,<br \/>\r\ntitle = {Performing Bayesian Inference by Weighted Model Counting.},<br \/>\r\nauthor = {Tian Sang and Paul Beame and Henry Kautz},<br \/>\r\ndoi = {10.5555\/1619332.1619409},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-08-01},<br \/>\r\nurldate = {2005-08-01},<br \/>\r\nbooktitle = {Proceedings, AAAI-05: Twentieth National Conference on Artificial Intelligence},<br \/>\r\npages = {475-482},<br \/>\r\naddress = {Pittsburgh, PA},<br \/>\r\norganization = {American Association for Artificial Intelligence},<br \/>\r\ncrossref = {aaai05},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('176','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_176\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.5555\/1619332.1619409\" title=\"Follow DOI:10.5555\/1619332.1619409\" target=\"_blank\">doi:10.5555\/1619332.1619409<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('176','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Culberson, Joe;  Mitchell, David;  Moore, Cristopher<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('49','tp_links')\" style=\"cursor:pointer;\">The Resolution Complexity of Random Graph $k$-Colorability<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Discrete Applied Mathematics, <\/span><span class=\"tp_pub_additional_volume\">vol. 153, <\/span><span class=\"tp_pub_additional_pages\">pp. 25\u201347, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_49\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('49','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_49\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bcmm:color,<br \/>\r\ntitle = {The Resolution Complexity of Random Graph $k$-Colorability},<br \/>\r\nauthor = {Paul Beame and Joe Culberson and David Mitchell and Cristopher Moore},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kcolor.pdf},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-01-01},<br \/>\r\njournal = {Discrete Applied Mathematics},<br \/>\r\nvolume = {153},<br \/>\r\npages = {25\u201347},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('49','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_49\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kcolor.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kcolor.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kcolor.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('49','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('126','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR05-053, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_126\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('126','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_126\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bps:kfoldtseitin-eccc,<br \/>\r\ntitle = {Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-01-01},<br \/>\r\nnumber = {TR05-053},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('126','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_126\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-053\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('126','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('127','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Automata, Languages, and Programming: 32nd International Colloquium (ICALP 2005), <\/span><span class=\"tp_pub_additional_pages\">pp. 1176\u20131188, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_127\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('127','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_127\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bps:kfoldtseitin,<br \/>\r\ntitle = {Lower Bounds for Lov\u00e1sz-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-01-01},<br \/>\r\nbooktitle = {Automata, Languages, and Programming: 32nd International Colloquium (ICALP 2005)},<br \/>\r\npages = {1176\u20131188},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('127','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_127\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/kfoldtseitin.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('127','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Sang, Tian;  Beame, Paul;  Kautz, Henry<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('177','tp_links')\" style=\"cursor:pointer;\">Heuristics for fast exact model counting<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Bacchus, Fahiem;  Walsh, Toby (Ed.): <span class=\"tp_pub_additional_booktitle\">Theory and Applications of Satisfiability Testing, 8th International Conference, SAT 2005, St Andrews, UK, June 2005. Proceedings, <\/span><span class=\"tp_pub_additional_pages\">pp. 226\u2013240, <\/span><span class=\"tp_pub_additional_year\">2005<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_177\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('177','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_177\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{sbk:heuristics,<br \/>\r\ntitle = {Heuristics for fast exact model counting},<br \/>\r\nauthor = {Tian Sang and Paul Beame and Henry Kautz},<br \/>\r\neditor = {Fahiem Bacchus and Toby Walsh},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet-heuristics.pdf},<br \/>\r\nyear  = {2005},<br \/>\r\ndate = {2005-01-01},<br \/>\r\nbooktitle = {Theory and Applications of Satisfiability Testing, 8th International Conference, SAT 2005, St Andrews, UK, June 2005. Proceedings},<br \/>\r\nvolume = {3569},<br \/>\r\npages = {226\u2013240},<br \/>\r\ncrossref = {SAT05},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('177','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_177\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet-heuristics.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet-heuristics.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet-heuristics.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('177','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Achlioptas, Dimitris;  Beame, Paul;  Molloy, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('3','tp_links')\" style=\"cursor:pointer;\">A sharp threshold in proof complexity yields lower bounds for satisfiability search<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Computer and System Sciences, <\/span><span class=\"tp_pub_additional_volume\">vol. 68, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 238\u2013268, <\/span><span class=\"tp_pub_additional_year\">2004<\/span><span class=\"tp_pub_additional_note\">, (Special issue of invited papers from STOC 2001 conference)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_3\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('3','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_3\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{abm:2+psat-journal,<br \/>\r\ntitle = {A sharp threshold in proof complexity yields lower bounds for satisfiability search},<br \/>\r\nauthor = {Dimitris Achlioptas and Paul Beame and Michael Molloy},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/2plusp.pdf},<br \/>\r\nyear  = {2004},<br \/>\r\ndate = {2004-03-01},<br \/>\r\njournal = {Journal of Computer and System Sciences},<br \/>\r\nvolume = {68},<br \/>\r\nnumber = {2},<br \/>\r\npages = {238\u2013268},<br \/>\r\nnote = {Special issue of invited papers from STOC 2001 conference},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('3','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_3\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/2plusp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/2plusp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/2plusp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('3','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Achlioptas, Dimitris;  Beame, Paul;  Molloy, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('4','tp_links')\" style=\"cursor:pointer;\">Exponential Bounds for DPLL Below the Satisfiability Threshold<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, <\/span><span class=\"tp_pub_additional_pages\">pp. 139\u2013140, <\/span><span class=\"tp_pub_additional_address\">New Orleans, LA, <\/span><span class=\"tp_pub_additional_year\">2004<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_4\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('4','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_4\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{abm:hardsat,<br \/>\r\ntitle = {Exponential Bounds for DPLL Below the Satisfiability Threshold},<br \/>\r\nauthor = {Dimitris Achlioptas and Paul Beame and Michael Molloy},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/soda04.pdf},<br \/>\r\nyear  = {2004},<br \/>\r\ndate = {2004-01-01},<br \/>\r\nbooktitle = {Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms},<br \/>\r\npages = {139\u2013140},<br \/>\r\naddress = {New Orleans, LA},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('4','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_4\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/soda04.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/soda04.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/soda04.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('4','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_incollection\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('22','tp_links')\" style=\"cursor:pointer;\">Proof Complexity<\/a> <span class=\"tp_pub_type tp_  incollection\">Book Section<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Rudich, Steven;  Wigderson, Avi (Ed.): <span class=\"tp_pub_additional_booktitle\">Computational Complexity Theory, <\/span><span class=\"tp_pub_additional_volume\">vol. 10, <\/span><span class=\"tp_pub_additional_pages\">pp. 199\u2013246, <\/span><span class=\"tp_pub_additional_publisher\">American Mathematical Society, <\/span><span class=\"tp_pub_additional_year\">2004<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_22\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('22','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_22\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@incollection{beame:parkcity,<br \/>\r\ntitle = {Proof Complexity},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\neditor = {Steven Rudich and Avi Wigderson},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/lec.pdf},<br \/>\r\nyear  = {2004},<br \/>\r\ndate = {2004-01-01},<br \/>\r\nbooktitle = {Computational Complexity Theory},<br \/>\r\nvolume = {10},<br \/>\r\npages = {199\u2013246},<br \/>\r\npublisher = {American Mathematical Society},<br \/>\r\nseries = {IAS\/Park City mathematics series},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {incollection}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('22','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_22\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/lec.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/lec.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/lec.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('22','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Culberson, Joe;  Mitchell, David;  Moore, Cristopher<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('50','tp_links')\" style=\"cursor:pointer;\">The Resolution Complexity of Random Graph $k$-Colorability<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR04-012, <\/span><span class=\"tp_pub_additional_year\">2004<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_50\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('50','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_50\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bcmm:color-eccc,<br \/>\r\ntitle = {The Resolution Complexity of Random Graph $k$-Colorability},<br \/>\r\nauthor = {Paul Beame and Joe Culberson and David Mitchell and Cristopher Moore},<br \/>\r\nurl = {http:\/\/eccc.uni-trier.de\/eccc-reports\/2004\/TR04-012\/index.html},<br \/>\r\nyear  = {2004},<br \/>\r\ndate = {2004-01-01},<br \/>\r\nnumber = {TR04-012},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('50','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_50\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2004\/TR04-012\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2004\/TR04-012\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2004\/TR04-012\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('50','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kautz, Henry;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('90','tp_links')\" style=\"cursor:pointer;\">Towards understanding and harnessing the potential of clause learning<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Artificial Intelligence Research, <\/span><span class=\"tp_pub_additional_volume\">vol. 22, <\/span><span class=\"tp_pub_additional_pages\">pp. 319\u2013351, <\/span><span class=\"tp_pub_additional_year\">2004<\/span><span class=\"tp_pub_additional_note\">, (Honorable mention (sole runner up) 2008 IJCAI-JAIR Best Paper Prize)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_90\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('90','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_90\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:learn-journal,<br \/>\r\ntitle = {Towards understanding and harnessing the potential of clause learning},<br \/>\r\nauthor = {Paul Beame and Henry Kautz and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnJAIRfinal.pdf},<br \/>\r\nyear  = {2004},<br \/>\r\ndate = {2004-01-01},<br \/>\r\njournal = {Journal of Artificial Intelligence Research},<br \/>\r\nvolume = {22},<br \/>\r\npages = {319\u2013351},<br \/>\r\nnote = {Honorable mention (sole runner up) 2008 IJCAI-JAIR Best Paper Prize},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('90','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_90\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnJAIRfinal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnJAIRfinal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnJAIRfinal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('90','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Buresh-Oppenheim, Joshua;  Beame, Paul;  Pitassi, Toniann;  Raz, Ran;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('168','tp_links')\" style=\"cursor:pointer;\">Bounded-depth Frege lower bounds for weaker pigeonhole principles<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 34, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 261\u2013276, <\/span><span class=\"tp_pub_additional_year\">2004<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_168\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('168','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_168\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbprs:wphp-journal,<br \/>\r\ntitle = {Bounded-depth Frege lower bounds for weaker pigeonhole principles},<br \/>\r\nauthor = {Joshua Buresh-Oppenheim and Paul Beame and Toniann Pitassi and Ran Raz and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wphp.pdf},<br \/>\r\nyear  = {2004},<br \/>\r\ndate = {2004-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {34},<br \/>\r\nnumber = {2},<br \/>\r\npages = {261\u2013276},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('168','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_168\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wphp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wphp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/wphp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('168','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Sang, Tian;  Bacchus, Fahiem;  Beame, Paul;  Kautz, Henry;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('175','tp_links')\" style=\"cursor:pointer;\">Combining Component Caching and Clause Learning for Effective Model Counting<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">SAT 2004, Satisfiability Conference, <\/span><span class=\"tp_pub_additional_pages\">pp. 20\u201328, <\/span><span class=\"tp_pub_additional_year\">2004<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_175\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('175','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_175\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{sbbkp:numsat,<br \/>\r\ntitle = {Combining Component Caching and Clause Learning for Effective Model Counting},<br \/>\r\nauthor = {Tian Sang and Fahiem Bacchus and Paul Beame and Henry Kautz and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet.pdf},<br \/>\r\nyear  = {2004},<br \/>\r\ndate = {2004-01-01},<br \/>\r\nbooktitle = {SAT 2004, Satisfiability Conference},<br \/>\r\npages = {20\u201328},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('175','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_175\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cachet.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('175','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kautz, Henry;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('89','tp_links')\" style=\"cursor:pointer;\">On the power of clause learning<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 18th International Joint Conference in \r\n Artificial Intelligence (IJCAI), <\/span><span class=\"tp_pub_additional_pages\">pp. 94\u201399, <\/span><span class=\"tp_pub_additional_address\">Acapulco, Mexico, <\/span><span class=\"tp_pub_additional_year\">2003<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_89\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('89','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_89\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bks:learn,<br \/>\r\ntitle = {On the power of clause learning},<br \/>\r\nauthor = {Paul Beame and Henry Kautz and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ijcai03.pdf},<br \/>\r\nyear  = {2003},<br \/>\r\ndate = {2003-08-01},<br \/>\r\nbooktitle = {Proceedings of the 18th International Joint Conference in <br \/>\r\n Artificial Intelligence (IJCAI)},<br \/>\r\npages = {94\u201399},<br \/>\r\naddress = {Acapulco, Mexico},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('89','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_89\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ijcai03.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ijcai03.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ijcai03.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('89','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Pitassi, Toniann;  Segerlind, Nathan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('73','tp_links')\" style=\"cursor:pointer;\">Memoization and DPLL: Formula Caching Proof Systems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings Eighteenth Annual IEEE Conference on Computational Complexity, <\/span><span class=\"tp_pub_additional_pages\">pp. 225\u2013236, <\/span><span class=\"tp_pub_additional_address\">Aarhus, Denmark, <\/span><span class=\"tp_pub_additional_year\">2003<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_73\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('73','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_73\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bips:caching,<br \/>\r\ntitle = {Memoization and DPLL: Formula Caching Proof Systems},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Toniann Pitassi and Nathan Segerlind},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching.pdf},<br \/>\r\nyear  = {2003},<br \/>\r\ndate = {2003-07-01},<br \/>\r\nbooktitle = {Proceedings Eighteenth Annual IEEE Conference on Computational Complexity},<br \/>\r\npages = {225\u2013236},<br \/>\r\naddress = {Aarhus, Denmark},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('73','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_73\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/caching.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('73','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Sabharwal, Ashish;  Beame, Paul;  Kautz, Henry<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('174','tp_links')\" style=\"cursor:pointer;\">Using Problem Structure for Efficient Clause Learning<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Sixth International Conference on Theory and Applications of Satisfiability Testing (SAT 2003), <\/span><span class=\"tp_pub_additional_pages\">pp. 159\u2013166, <\/span><span class=\"tp_pub_additional_year\">2003<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_174\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('174','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_174\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{sbk:learnsat,<br \/>\r\ntitle = {Using Problem Structure for Efficient Clause Learning},<br \/>\r\nauthor = {Ashish Sabharwal and Paul Beame and Henry Kautz},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnSAT03.pdf},<br \/>\r\nyear  = {2003},<br \/>\r\ndate = {2003-01-01},<br \/>\r\nbooktitle = {Proceedings of the Sixth International Conference on Theory and Applications of Satisfiability Testing (SAT 2003)},<br \/>\r\npages = {159\u2013166},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('174','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_174\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnSAT03.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnSAT03.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/learnSAT03.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('174','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Buresh-Oppenheim, Joshua;  Beame, Paul;  Pitassi, Toniann;  Raz, Ran;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('167','tp_links')\" style=\"cursor:pointer;\">Bounded-depth Frege lower bounds for weaker pigeonhole principles<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 43rd Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 583\u2013592, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Vancouver, B.C., Canada, <\/span><span class=\"tp_pub_additional_year\">2002<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_167\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('167','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_167\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bbprs:wphp,<br \/>\r\ntitle = {Bounded-depth Frege lower bounds for weaker pigeonhole principles},<br \/>\r\nauthor = {Joshua Buresh-Oppenheim and Paul Beame and Toniann Pitassi and Ran Raz and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focswphp.pdf},<br \/>\r\nyear  = {2002},<br \/>\r\ndate = {2002-11-01},<br \/>\r\nbooktitle = {Proceedings 43rd Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {583\u2013592},<br \/>\r\naddress = {Vancouver, B.C., Canada},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('167','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_167\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focswphp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focswphp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focswphp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('167','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Karp, Richard;  Pitassi, Toniann;  Saks, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('163','tp_links')\" style=\"cursor:pointer;\">The efficiency of resolution and Davis-Putnam procedures<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 31, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 1048\u20131075, <\/span><span class=\"tp_pub_additional_year\">2002<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_163\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('163','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_163\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bkps:resolve-journal,<br \/>\r\ntitle = {The efficiency of resolution and Davis-Putnam procedures},<br \/>\r\nauthor = {Paul Beame and Richard Karp and Toniann Pitassi and Michael Saks},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/resj.pdf},<br \/>\r\nyear  = {2002},<br \/>\r\ndate = {2002-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {31},<br \/>\r\nnumber = {4},<br \/>\r\npages = {1048\u20131075},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('163','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_163\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/resj.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/resj.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/resj.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('163','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Buresh-Oppenheim, Joshua;  Beame, Paul;  Pitassi, Toniann;  Raz, Ran;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('166','tp_links')\" style=\"cursor:pointer;\">Bounded-depth Frege lower bounds for weaker pigeonhole principles<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR02-023, <\/span><span class=\"tp_pub_additional_year\">2002<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_166\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('166','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_166\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bbprs:wphp-eccc,<br \/>\r\ntitle = {Bounded-depth Frege lower bounds for weaker pigeonhole principles},<br \/>\r\nauthor = {Joshua Buresh-Oppenheim and Paul Beame and Toniann Pitassi and Ran Raz and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/eccc.uni-trier.de\/eccc-reports\/2002\/TR02-023\/index.html},<br \/>\r\nyear  = {2002},<br \/>\r\ndate = {2002-01-01},<br \/>\r\nnumber = {TR02-023},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('166','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_166\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2002\/TR02-023\/index.html\" title=\"http:\/\/eccc.uni-trier.de\/eccc-reports\/2002\/TR02-023\/index.html\" target=\"_blank\">http:\/\/eccc.uni-trier.de\/eccc-reports\/2002\/TR02-023\/index.html<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('166','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Achlioptas, Dimitris;  Beame, Paul;  Molloy, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('1','tp_links')\" style=\"cursor:pointer;\">A sharp threshold in proof complexity<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 337\u2013346, <\/span><span class=\"tp_pub_additional_address\">Heraklion, Crete, Greece, <\/span><span class=\"tp_pub_additional_year\">2001<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_1\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('1','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_1\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{abm:2+psat,<br \/>\r\ntitle = {A sharp threshold in proof complexity},<br \/>\r\nauthor = {Dimitris Achlioptas and Paul Beame and Michael Molloy},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoc2plusp.pdf},<br \/>\r\nyear  = {2001},<br \/>\r\ndate = {2001-07-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {337\u2013346},<br \/>\r\naddress = {Heraklion, Crete, Greece},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_1\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoc2plusp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoc2plusp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoc2plusp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('1','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Sabharwal, Ashish<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('76','tp_links')\" style=\"cursor:pointer;\">The Resolution Complexity of the Independent Set Problem in Random Graphs<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings Sixteenth Annual IEEE Conference on Computational Complexity, <\/span><span class=\"tp_pub_additional_pages\">pp. 52-68, <\/span><span class=\"tp_pub_additional_address\">Chicago, IL, <\/span><span class=\"tp_pub_additional_year\">2001<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_76\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('76','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_76\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bis:independent,<br \/>\r\ntitle = {The Resolution Complexity of the Independent Set Problem in Random Graphs},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Ashish Sabharwal},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cccindep.pdf},<br \/>\r\nyear  = {2001},<br \/>\r\ndate = {2001-06-01},<br \/>\r\nbooktitle = {Proceedings Sixteenth Annual IEEE Conference on Computational Complexity},<br \/>\r\npages = {52-68},<br \/>\r\naddress = {Chicago, IL},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('76','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_76\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cccindep.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cccindep.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/cccindep.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('76','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_incollection\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('123','tp_links')\" style=\"cursor:pointer;\">Propositional Proof Complexity: Past, Present, and Future<\/a> <span class=\"tp_pub_type tp_  incollection\">Book Section<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Paun, G.;  Rozenberg, G.;  Salomaa, A. (Ed.): <span class=\"tp_pub_additional_booktitle\">Current Trends in Theoretical Computer Science: \r\n Entering the 21st Century, <\/span><span class=\"tp_pub_additional_pages\">pp. 42\u201370, <\/span><span class=\"tp_pub_additional_publisher\">World Scientific Publishing, <\/span><span class=\"tp_pub_additional_year\">2001<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_123\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('123','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_123\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@incollection{bp:survey-world,<br \/>\r\ntitle = {Propositional Proof Complexity: Past, Present, and Future},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi},<br \/>\r\neditor = {G. Paun and G. Rozenberg and A. Salomaa},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofsurvey.pdf},<br \/>\r\nyear  = {2001},<br \/>\r\ndate = {2001-01-01},<br \/>\r\nbooktitle = {Current Trends in Theoretical Computer Science: <br \/>\r\n Entering the 21st Century},<br \/>\r\npages = {42\u201370},<br \/>\r\npublisher = {World Scientific Publishing},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {incollection}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('123','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_123\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofsurvey.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofsurvey.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/proofsurvey.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('123','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('122','tp_links')\" style=\"cursor:pointer;\">Propositional Proof Complexity: Past, Present, and Future<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Bulletin of the European Association for Theoretical Computer Science, <\/span><span class=\"tp_pub_additional_volume\">vol. 65, <\/span><span class=\"tp_pub_additional_year\">1998<\/span><span class=\"tp_pub_additional_note\">, (The Computational Complexity Column (ed. E. Allender).)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_122\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('122','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_122\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bp:survey-eatcs,<br \/>\r\ntitle = {Propositional Proof Complexity: Past, Present, and Future},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/eatcs-survey.ps},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-06-01},<br \/>\r\njournal = {Bulletin of the European Association for Theoretical Computer Science},<br \/>\r\nvolume = {65},<br \/>\r\nnote = {The Computational Complexity Column (ed. E. Allender).},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('122','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_122\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/eatcs-survey.ps\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/eatcs-survey.ps\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/eatcs-survey.ps<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('122','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Karp, Richard;  Pitassi, Toniann;  Saks, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('162','tp_links')\" style=\"cursor:pointer;\">On the complexity of unsatisfiability of random $k$-CNF formulas<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 30th Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 561-571, <\/span><span class=\"tp_pub_additional_address\">Dallas, TX, <\/span><span class=\"tp_pub_additional_year\">1998<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_162\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('162','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_162\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bkps:kcnf,<br \/>\r\ntitle = {On the complexity of unsatisfiability of random $k$-CNF formulas},<br \/>\r\nauthor = {Paul Beame and Richard Karp and Toniann Pitassi and Michael Saks},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stockcnf.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-05-01},<br \/>\r\nbooktitle = {Proceedings of the 30th Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {561-571},<br \/>\r\naddress = {Dallas, TX},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('162','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_162\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stockcnf.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stockcnf.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stockcnf.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('162','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_book\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Buss, Samuel R. (Ed.)<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('30','tp_links')\" style=\"cursor:pointer;\">Proof Complexity and Feasible Arithmetics<\/a> <span class=\"tp_pub_type tp_  book\">Book<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_publisher\">American Mathematical Society, <\/span><span class=\"tp_pub_additional_year\">1998<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_30\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('30','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_30\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@book{bb:proofcomp,<br \/>\r\ntitle = {Proof Complexity and Feasible Arithmetics},<br \/>\r\neditor = {Paul Beame and Samuel R. Buss},<br \/>\r\nurl = {http:\/\/www.ams.org\/bookstore?fn=20&arg1=logfound&ikey=DIMACS-39},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-01-01},<br \/>\r\nbooktitle = {Proof Complexity and Feasible Arithmetics},<br \/>\r\nvolume = {39},<br \/>\r\npublisher = {American Mathematical Society},<br \/>\r\nseries = {DIMACS Series in Discrete Mathematics and Theoretical Computer <br \/>\r\n Science},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {book}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('30','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_30\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.ams.org\/bookstore?fn=20&amp;arg1=logfound&amp;ikey=DIMACS-39\" title=\"http:\/\/www.ams.org\/bookstore?fn=20&amp;arg1=logfound&amp;ikey=DIMACS-39\" target=\"_blank\">http:\/\/www.ams.org\/bookstore?fn=20&amp;arg1=logfound&amp;ikey=DIMACS-39<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('30','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Cook, Stephen A.;  Edmonds, Jeff;  Impagliazzo, Russell;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('45','tp_links')\" style=\"cursor:pointer;\">The Relative Complexity of NP Search Problems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Computer and System Sciences, <\/span><span class=\"tp_pub_additional_volume\">vol. 57, <\/span><span class=\"tp_pub_additional_pages\">pp. 3\u201319, <\/span><span class=\"tp_pub_additional_year\">1998<\/span><span class=\"tp_pub_additional_note\">, (Special issue of invited papers from 1995 STOC conference.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_45\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('45','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_45\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bceip:search-journal,<br \/>\r\ntitle = {The Relative Complexity of NP Search Problems},<br \/>\r\nauthor = {Paul Beame and Stephen A. Cook and Jeff Edmonds and Russell Impagliazzo and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-01-01},<br \/>\r\nurldate = {1998-01-01},<br \/>\r\njournal = {Journal of Computer and System Sciences},<br \/>\r\nvolume = {57},<br \/>\r\npages = {3\u201319},<br \/>\r\nnote = {Special issue of invited papers from 1995 STOC conference.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('45','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_45\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('45','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_incollection\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Riis, S\u00f8ren<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('161','tp_links')\" style=\"cursor:pointer;\">More on the Relative Strength of Counting Principles<\/a> <span class=\"tp_pub_type tp_  incollection\">Book Section<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Beame, Paul W.;  Buss, Samuel R. (Ed.): <span class=\"tp_pub_additional_booktitle\">Proof Complexity and Feasible Arithmetics, <\/span><span class=\"tp_pub_additional_volume\">vol. 39, <\/span><span class=\"tp_pub_additional_pages\">pp. 13-35, <\/span><span class=\"tp_pub_additional_publisher\">American Mathematical Society, <\/span><span class=\"tp_pub_additional_year\">1998<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_161\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('161','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_161\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@incollection{br:count,<br \/>\r\ntitle = {More on the Relative Strength of Counting Principles},<br \/>\r\nauthor = {Paul Beame and S\u00f8ren Riis},<br \/>\r\neditor = {Paul W. Beame and Samuel R. Buss},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/riis.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-01-01},<br \/>\r\nbooktitle = {Proof Complexity and Feasible Arithmetics},<br \/>\r\nvolume = {39},<br \/>\r\npages = {13-35},<br \/>\r\npublisher = {American Mathematical Society},<br \/>\r\nseries = {DIMACS Series in Discrete Mathematics and Theoretical Computer Science},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {incollection}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('161','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_161\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/riis.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/riis.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/riis.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('161','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('158','tp_links')\" style=\"cursor:pointer;\">Simplified and Improved Resolution Lower Bounds<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 37th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 274\u2013282, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Burlington, VT, <\/span><span class=\"tp_pub_additional_year\">1996<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_158\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('158','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_158\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bp:resolve,<br \/>\r\ntitle = {Simplified and Improved Resolution Lower Bounds},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsclause.pdf},<br \/>\r\nyear  = {1996},<br \/>\r\ndate = {1996-10-01},<br \/>\r\nbooktitle = {Proceedings 37th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {274\u2013282},<br \/>\r\naddress = {Burlington, VT},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('158','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_158\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsclause.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsclause.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsclause.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('158','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Kraj\u00ed\u010dek, Jan;  Pitassi, Toniann;  Pudl\u00e1k, Pavel<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('70','tp_links')\" style=\"cursor:pointer;\">Lower bounds on Hilbert's Nullstellensatz and propositional \r\n proofs<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Proc. London Math. Soc., <\/span><span class=\"tp_pub_additional_volume\">vol. 73, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 1\u201326, <\/span><span class=\"tp_pub_additional_year\">1996<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_70\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('70','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_70\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bikpp:nsatzjournal,<br \/>\r\ntitle = {Lower bounds on Hilbert's Nullstellensatz and propositional <br \/>\r\n proofs},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Jan Kraj\u00ed\u010dek and Toniann Pitassi and Pavel Pudl\u00e1k},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nsatz.pdf},<br \/>\r\nyear  = {1996},<br \/>\r\ndate = {1996-01-01},<br \/>\r\njournal = {Proc. London Math. Soc.},<br \/>\r\nvolume = {73},<br \/>\r\nnumber = {3},<br \/>\r\npages = {1\u201326},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('70','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_70\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nsatz.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nsatz.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/nsatz.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('70','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('121','tp_links')\" style=\"cursor:pointer;\">An Exponential Separation between the Parity Principle and the \r\n Pigeonhole Principle<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Annals of Pure and Applied Logic, <\/span><span class=\"tp_pub_additional_volume\">vol. 80, <\/span><span class=\"tp_pub_additional_pages\">pp. 197-222, <\/span><span class=\"tp_pub_additional_year\">1996<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_121\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('121','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_121\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bp:parity,<br \/>\r\ntitle = {An Exponential Separation between the Parity Principle and the <br \/>\r\n Pigeonhole Principle},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/parity.pdf},<br \/>\r\nyear  = {1996},<br \/>\r\ndate = {1996-01-01},<br \/>\r\njournal = {Annals of Pure and Applied Logic},<br \/>\r\nvolume = {80},<br \/>\r\npages = {197-222},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('121','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_121\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/parity.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/parity.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/parity.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('121','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Cook, Stephen A.;  Edmonds, Jeff;  Impagliazzo, Russell;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('44','tp_links')\" style=\"cursor:pointer;\">The Relative Complexity of NP Search Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 303\u2013314, <\/span><span class=\"tp_pub_additional_address\">Las Vegas, NV, <\/span><span class=\"tp_pub_additional_year\">1995<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_44\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('44','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_44\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bceip:search,<br \/>\r\ntitle = {The Relative Complexity of NP Search Problems},<br \/>\r\nauthor = {Paul Beame and Stephen A. Cook and Jeff Edmonds and Russell Impagliazzo and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf},<br \/>\r\nyear  = {1995},<br \/>\r\ndate = {1995-05-01},<br \/>\r\nbooktitle = {Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {303\u2013314},<br \/>\r\naddress = {Las Vegas, NV},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('44','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_44\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('44','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Kraj\u00ed\u010dek, Jan;  Pitassi, Toniann;  Pudl\u00e1k, Pavel<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('69','tp_links')\" style=\"cursor:pointer;\">Lower bounds on Hilbert's Nullstellensatz and propositional proofs<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 35th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 794-806, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Santa Fe, NM, <\/span><span class=\"tp_pub_additional_year\">1994<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_69\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('69','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_69\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bikpp:nsatz,<br \/>\r\ntitle = {Lower bounds on Hilbert's Nullstellensatz and propositional proofs},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Jan Kraj\u00ed\u010dek and Toniann Pitassi and Pavel Pudl\u00e1k},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsstell.pdf},<br \/>\r\nyear  = {1994},<br \/>\r\ndate = {1994-11-01},<br \/>\r\nbooktitle = {Proceedings 35th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {794-806},<br \/>\r\naddress = {Santa Fe, NM},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('69','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_69\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsstell.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsstell.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsstell.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('69','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('119','tp_links')\" style=\"cursor:pointer;\">An Exponential Separation between the Matching Principle and the \r\n Pigeonhole Principle<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">8th Annual IEEE Symposium on Logic in Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 308\u2013319, <\/span><span class=\"tp_pub_additional_address\">Montreal, Quebec, <\/span><span class=\"tp_pub_additional_year\">1993<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_119\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('119','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_119\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bp93,<br \/>\r\ntitle = {An Exponential Separation between the Matching Principle and the <br \/>\r\n Pigeonhole Principle},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/licsmatch.pdf},<br \/>\r\nyear  = {1993},<br \/>\r\ndate = {1993-06-01},<br \/>\r\nbooktitle = {8th Annual IEEE Symposium on Logic in Computer Science},<br \/>\r\npages = {308\u2013319},<br \/>\r\naddress = {Montreal, Quebec},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('119','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_119\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/licsmatch.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/licsmatch.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/licsmatch.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('119','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\">An Exponential Separation between the Matching Principle and the \r\n Pigeonhole Principle <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Department of Computer Science and Engineering, University of Washington <\/span><span class=\"tp_pub_additional_number\">no. UW-CSE-93-04-07, <\/span><span class=\"tp_pub_additional_year\">1993<\/span>.<\/p><p class=\"tp_pub_menu\"><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_120\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bp93-tr,<br \/>\r\ntitle = {An Exponential Separation between the Matching Principle and the <br \/>\r\n Pigeonhole Principle},<br \/>\r\nauthor = {Paul Beame and Toniann Pitassi},<br \/>\r\nyear  = {1993},<br \/>\r\ndate = {1993-04-01},<br \/>\r\nnumber = {UW-CSE-93-04-07},<br \/>\r\ninstitution = {Department of Computer Science and Engineering, University of Washington},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('120','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Pitassi, Toniann;  Beame, Paul;  Impagliazzo, Russell<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('170','tp_links')\" style=\"cursor:pointer;\">Exponential Lower Bounds for the Pigeonhole Principle<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Computational Complexity, <\/span><span class=\"tp_pub_additional_volume\">vol. 3, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 97\u2013140, <\/span><span class=\"tp_pub_additional_year\">1993<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_170\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('170','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_170\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{pbi93,<br \/>\r\ntitle = {Exponential Lower Bounds for the Pigeonhole Principle},<br \/>\r\nauthor = {Toniann Pitassi and Paul Beame and Russell Impagliazzo},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/php.pdf},<br \/>\r\nyear  = {1993},<br \/>\r\ndate = {1993-01-01},<br \/>\r\njournal = {Computational Complexity},<br \/>\r\nvolume = {3},<br \/>\r\nnumber = {2},<br \/>\r\npages = {97\u2013140},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('170','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_170\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/php.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/php.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/php.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('170','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Kraj\u00ed\u010dek, Jan;  Pitassi, Toniann;  Pudl\u00e1k, Pavel;  Woods, Alan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('68','tp_links')\" style=\"cursor:pointer;\">Exponential Lower Bounds for the Pigeonhole Principle<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 200-220, <\/span><span class=\"tp_pub_additional_address\">Victoria, B.C., Canada, <\/span><span class=\"tp_pub_additional_year\">1992<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_68\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('68','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_68\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bikppw92,<br \/>\r\ntitle = {Exponential Lower Bounds for the Pigeonhole Principle},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Jan Kraj\u00ed\u010dek and Toniann Pitassi and Pavel Pudl\u00e1k and Alan Woods},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocphp.pdf},<br \/>\r\nyear  = {1992},<br \/>\r\ndate = {1992-05-01},<br \/>\r\nbooktitle = {Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {200-220},<br \/>\r\naddress = {Victoria, B.C., Canada},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('68','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_68\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocphp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocphp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocphp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('68','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-parallel\"><strong>Parallel and Distributed Computing<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_incollection\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  McKenzie, Pierre<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('118','tp_links')\" style=\"cursor:pointer;\">Towards a Complexity Theory of Parallel Computation<\/a> <span class=\"tp_pub_type tp_  incollection\">Book Section<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span> Kapron, Bruce M. (Ed.): <span class=\"tp_pub_additional_booktitle\">Logic, Automata, and Computational Complexity: The Works of Stephen A. Cook, <\/span><span class=\"tp_pub_additional_pages\">pp. 107\u2013126, <\/span><span class=\"tp_pub_additional_publisher\">Association for Computing Machinery, <\/span><span class=\"tp_pub_additional_address\">New York, NY, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_118\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('118','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_118\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@incollection{bm:cook-parallel,<br \/>\r\ntitle = {Towards a Complexity Theory of Parallel Computation},<br \/>\r\nauthor = {Paul Beame and Pierre McKenzie},<br \/>\r\neditor = {Bruce M. Kapron},<br \/>\r\nurl = {https:\/\/dl.acm.org\/doi\/10.1145\/3588287.3588295},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-01-01},<br \/>\r\nbooktitle = {Logic, Automata, and Computational Complexity: The Works of Stephen A. Cook},<br \/>\r\npages = {107\u2013126},<br \/>\r\npublisher = {Association for Computing Machinery},<br \/>\r\naddress = {New York, NY},<br \/>\r\nchapter = {7},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {incollection}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('118','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_118\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dl.acm.org\/doi\/10.1145\/3588287.3588295\" title=\"https:\/\/dl.acm.org\/doi\/10.1145\/3588287.3588295\" target=\"_blank\">https:\/\/dl.acm.org\/doi\/10.1145\/3588287.3588295<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('118','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('92','tp_links')\" style=\"cursor:pointer;\">Communication Steps for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of the ACM, <\/span><span class=\"tp_pub_additional_volume\">vol. 64, <\/span><span class=\"tp_pub_additional_number\">no. 6, <\/span><span class=\"tp_pub_additional_pages\">pp. 40:1-58, <\/span><span class=\"tp_pub_additional_year\">2017<\/span><span class=\"tp_pub_additional_note\">, (Preliminary material in Proceedings of 2013 and 2014 ACM Symposium on Principles of Database Systems.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_92\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('92','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_92\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:mpc-journal,<br \/>\r\ntitle = {Communication Steps for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-10-01},<br \/>\r\njournal = {Journal of the ACM},<br \/>\r\nvolume = {64},<br \/>\r\nnumber = {6},<br \/>\r\npages = {40:1-58},<br \/>\r\nnote = {Preliminary material in Proceedings of 2013 and 2014 ACM Symposium on Principles of Database Systems.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('92','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_92\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpc-final.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('92','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Rashtchian, Cyrus<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('159','tp_links')\" style=\"cursor:pointer;\">Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, <\/span><span class=\"tp_pub_additional_pages\">pp. 289\u2013306, <\/span><span class=\"tp_pub_additional_address\">Barcelona, ES, <\/span><span class=\"tp_pub_additional_year\">2017<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_159\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('159','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_159\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{br:simjoin,<br \/>\r\ntitle = {Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube},<br \/>\r\nauthor = {Paul Beame and Cyrus Rashtchian},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf},<br \/>\r\nyear  = {2017},<br \/>\r\ndate = {2017-01-01},<br \/>\r\nbooktitle = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms},<br \/>\r\npages = {289\u2013306},<br \/>\r\naddress = {Barcelona, ES},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('159','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_159\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/simjoin-soda.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('159','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Rashtchian, Cyrus<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('160','tp_links')\" style=\"cursor:pointer;\">Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1611.04999, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_160\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('160','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_160\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{br:simjoin-tr,<br \/>\r\ntitle = {Massively-Parallel Similarity Join, Edge-Isoperimetry, and Distance Correlations on the Hypercube},<br \/>\r\nauthor = {Paul Beame and Cyrus Rashtchian},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1611.04999},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-11-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1611.04999},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('160','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_160\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1611.04999\" title=\"http:\/\/arxiv.org\/abs\/1611.04999\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1611.04999<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('160','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Koutris, Paraschos;  Beame, Paul;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('169','tp_links')\" style=\"cursor:pointer;\">Worst-Case Optimal Algorithms for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of 19th International Conference on Database Theory, <\/span><span class=\"tp_pub_additional_pages\">pp. 8:1\u20138:18, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_169\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('169','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_169\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{kbs:worst,<br \/>\r\ntitle = {Worst-Case Optimal Algorithms for Parallel Query Processing},<br \/>\r\nauthor = {Paraschos Koutris and Paul Beame and Dan Suciu},<br \/>\r\nurl = {http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-03-01},<br \/>\r\nbooktitle = {Proceedings of 19th International Conference on Database Theory},<br \/>\r\npages = {8:1\u20138:18},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('169','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_169\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8\" title=\"http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8\" target=\"_blank\">http:\/\/dx.doi.org\/10.4230\/LIPIcs.ICDT.2016.8<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('169','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('97','tp_links')\" style=\"cursor:pointer;\">Communication Cost in Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1602.06236, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_97\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('97','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_97\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:cost-arxiv,<br \/>\r\ntitle = {Communication Cost in Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1602.06236},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1602.06236},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('97','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_97\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1602.06236\" title=\"http:\/\/arxiv.org\/abs\/1602.06236\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1602.06236<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('97','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('98','tp_links')\" style=\"cursor:pointer;\">Worst-Case Optimal Algorithms for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1604.01848, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_98\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('98','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_98\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:worst-arxiv,<br \/>\r\ntitle = {Worst-Case Optimal Algorithms for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1604.01848},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1604.01848},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('98','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_98\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1604.01848\" title=\"http:\/\/arxiv.org\/abs\/1604.01848\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1604.01848<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('98','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('94','tp_links')\" style=\"cursor:pointer;\">Skew in Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Third Annual ACM Symposium on Principles of Database Systems, <\/span><span class=\"tp_pub_additional_pages\">pp. 212\u2013223, <\/span><span class=\"tp_pub_additional_address\">Snowbird, UT, <\/span><span class=\"tp_pub_additional_year\">2014<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_94\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('94','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_94\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bks:skew-pods,<br \/>\r\ntitle = {Skew in Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558},<br \/>\r\nyear  = {2014},<br \/>\r\ndate = {2014-06-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Third Annual ACM Symposium on Principles of Database Systems},<br \/>\r\npages = {212\u2013223},<br \/>\r\naddress = {Snowbird, UT},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('94','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_94\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558\" title=\"https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558\" target=\"_blank\">https:\/\/dl.acm.org\/doi\/10.1145\/2594538.2594558<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('94','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('95','tp_links')\" style=\"cursor:pointer;\">Skew in Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1401.1872, <\/span><span class=\"tp_pub_additional_year\">2014<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_95\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('95','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_95\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:skew-arxiv,<br \/>\r\ntitle = {Skew in Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1401.1872},<br \/>\r\nyear  = {2014},<br \/>\r\ndate = {2014-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1401.1872},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('95','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_95\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1401.1872\" title=\"http:\/\/arxiv.org\/abs\/1401.1872\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1401.1872<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('95','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('93','tp_links')\" style=\"cursor:pointer;\">Communication Steps for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Second Annual ACM Symposium on Principles of Database Systems, <\/span><span class=\"tp_pub_additional_pages\">pp. 273\u2013284, <\/span><span class=\"tp_pub_additional_address\">New York, NY, <\/span><span class=\"tp_pub_additional_year\">2013<\/span><span class=\"tp_pub_additional_note\">, (Winner of 2023 ACM PODS Alberto O. Mendelzon Test-of-Time Award.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_93\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('93','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_93\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bks:mpc-pods,<br \/>\r\ntitle = {Communication Steps for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-06-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Second Annual ACM Symposium on Principles of Database Systems},<br \/>\r\npages = {273\u2013284},<br \/>\r\naddress = {New York, NY},<br \/>\r\nnote = {Winner of 2023 ACM PODS Alberto O. Mendelzon Test-of-Time Award.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('93','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_93\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/mpcpods.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('93','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Koutris, Paraschos;  Suciu, Dan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('96','tp_links')\" style=\"cursor:pointer;\">Communication Steps for Parallel Query Processing<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1306.5972, <\/span><span class=\"tp_pub_additional_year\">2013<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_96\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('96','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_96\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bks:mpc-arxiv,<br \/>\r\ntitle = {Communication Steps for Parallel Query Processing},<br \/>\r\nauthor = {Paul Beame and Paraschos Koutris and Dan Suciu},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1306.5972},<br \/>\r\nyear  = {2013},<br \/>\r\ndate = {2013-01-01},<br \/>\r\nurldate = {2013-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1306.5972},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('96','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_96\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1306.5972\" title=\"http:\/\/arxiv.org\/abs\/1306.5972\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1306.5972<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('96','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Anderson, Richard J.;  Beame, Paul;  Brisson, Eric<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('7','tp_links')\" style=\"cursor:pointer;\">Parallel Algorithms for Arrangements<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Algorithmica, <\/span><span class=\"tp_pub_additional_volume\">vol. 15, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 104-125, <\/span><span class=\"tp_pub_additional_year\">1996<\/span><span class=\"tp_pub_additional_note\">, (Special issue of invited papers from 1990 SPAA conference)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_7\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('7','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_7\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('7','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_7\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{abb:arrange-journal,<br \/>\r\ntitle = {Parallel Algorithms for Arrangements},<br \/>\r\nauthor = {Richard J. Anderson and Paul Beame and Eric Brisson},<br \/>\r\neditor = {Paul Beame and Samuel R. Buss},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/arrangejournal.pdf <br \/>\r\nhttp:\/\/link.springer.com\/article\/10.1007%2FBF01941684},<br \/>\r\ndoi = {10.1145\/3416264 @techreportbbi:proofspace-eccc},<br \/>\r\nyear  = {1996},<br \/>\r\ndate = {1996-01-01},<br \/>\r\nbooktitle = {Proceedings Eighteenth Annual IEEE Conference on Computational Complexity},<br \/>\r\njournal = {Algorithmica},<br \/>\r\nvolume = {15},<br \/>\r\nnumber = {2},<br \/>\r\npages = {104-125},<br \/>\r\npublisher = {IEEE},<br \/>\r\naddress = {Aarhus, Denmark},<br \/>\r\ninstitution = {Electronic Colloquium in Computational Complexity},<br \/>\r\norganization = {IEEE},<br \/>\r\nschool = {University of Toronto},<br \/>\r\nseries = {DIMACS Series in Discrete Mathematics and Theoretical Computer <br \/>\r\n Science},<br \/>\r\ncrossref = {bch86\" <br \/>\r\na typo?? -JP @articlebch8},<br \/>\r\nabstract = {Introduces a task scheduling model which is useful in the design and analysis of algorithms for small parallel machines. The authors prove that under their model, the overhead experienced in scheduling an n*n grid graph is O(log log n) for p processors, p&gt;or=2. They also prove a matching lower bound of Omega (log logn) for p processors, p&gt;or=2. They give an extension of the model to cover the case where the processors can have varying speed or are subject to delay.},<br \/>\r\nnote = {Special issue of invited papers from 1990 SPAA conference},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('7','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_7\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Introduces a task scheduling model which is useful in the design and analysis of algorithms for small parallel machines. The authors prove that under their model, the overhead experienced in scheduling an n*n grid graph is O(log log n) for p processors, p&gt;or=2. They also prove a matching lower bound of Omega (log logn) for p processors, p&gt;or=2. They give an extension of the model to cover the case where the processors can have varying speed or are subject to delay.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('7','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_7\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/arrangejournal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/arrangejournal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/arrangejournal.pdf<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/link.springer.com\/article\/10.1007%2FBF01941684\" title=\"http:\/\/link.springer.com\/article\/10.1007%2FBF01941684\" target=\"_blank\">http:\/\/link.springer.com\/article\/10.1007%2FBF01941684<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1145\/3416264 @techreportbbi:proofspace-eccc\" title=\"Follow DOI:10.1145\/3416264 @techreportbbi:proofspace-eccc\" target=\"_blank\">doi:10.1145\/3416264 @techreportbbi:proofspace-eccc<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('7','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Kik, Marcin;  Kuty\u0142owski, Mirek<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('88','tp_links')\" style=\"cursor:pointer;\">Information Broadcasting by Exclusive Read PRAMs<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Parallel Processing Letters, <\/span><span class=\"tp_pub_additional_volume\">vol. 4, <\/span><span class=\"tp_pub_additional_number\">no. 1&amp;2, <\/span><span class=\"tp_pub_additional_pages\">pp. 159-169, <\/span><span class=\"tp_pub_additional_year\">1994<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_88\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('88','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_88\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bkk:broadcast,<br \/>\r\ntitle = {Information Broadcasting by Exclusive Read PRAMs},<br \/>\r\nauthor = {Paul Beame and Marcin Kik and Mirek Kuty\u0142owski},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/broadcast.ps <br \/>\r\nhttp:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012962649400017X},<br \/>\r\nyear  = {1994},<br \/>\r\ndate = {1994-01-01},<br \/>\r\njournal = {Parallel Processing Letters},<br \/>\r\nvolume = {4},<br \/>\r\nnumber = {1&2},<br \/>\r\npages = {159-169},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('88','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_88\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/broadcast.ps\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/broadcast.ps\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/broadcast.ps<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012962649400017X\" title=\"http:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012962649400017X\" target=\"_blank\">http:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S012962649400017X<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('88','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Brisson, Eric;  Ladner, Richard E.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('36','tp_links')\" style=\"cursor:pointer;\">The Complexity of Computing Symmetric Functions using Threshold Circuits<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Theoretical Computer Science, <\/span><span class=\"tp_pub_additional_volume\">vol. 100, <\/span><span class=\"tp_pub_additional_pages\">pp. 253-265, <\/span><span class=\"tp_pub_additional_year\">1992<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_36\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('36','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_36\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbl92,<br \/>\r\ntitle = {The Complexity of Computing Symmetric Functions using Threshold Circuits},<br \/>\r\nauthor = {Paul Beame and Eric Brisson and Richard E. Ladner},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf},<br \/>\r\nyear  = {1992},<br \/>\r\ndate = {1992-01-01},<br \/>\r\njournal = {Theoretical Computer Science},<br \/>\r\nvolume = {100},<br \/>\r\npages = {253-265},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('36','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_36\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('36','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Anderson, Richard J.;  Beame, Paul;  Brisson, Eric<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('5','tp_links')\" style=\"cursor:pointer;\">Parallel Algorithms for Arrangements<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures, <\/span><span class=\"tp_pub_additional_pages\">pp. 298-306, <\/span><span class=\"tp_pub_additional_address\">Crete, Greece, <\/span><span class=\"tp_pub_additional_year\">1990<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_5\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('5','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_5\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{abb:arrange,<br \/>\r\ntitle = {Parallel Algorithms for Arrangements},<br \/>\r\nauthor = {Richard J. Anderson and Paul Beame and Eric Brisson},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/spaaarrange.pdf},<br \/>\r\nyear  = {1990},<br \/>\r\ndate = {1990-06-01},<br \/>\r\nbooktitle = {Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures},<br \/>\r\npages = {298-306},<br \/>\r\naddress = {Crete, Greece},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('5','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_5\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/spaaarrange.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/spaaarrange.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/spaaarrange.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('5','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Anderson, Richard J.;  Beame, Paul;  Ruzzo, Walter L.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('8','tp_links')\" style=\"cursor:pointer;\">Low Overhead Parallel Schedules for Task Graphs<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures, <\/span><span class=\"tp_pub_additional_pages\">pp. 66-75, <\/span><span class=\"tp_pub_additional_address\">Crete, Greece, <\/span><span class=\"tp_pub_additional_year\">1990<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_8\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('8','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_8\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('8','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_8\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{abr:tasks,<br \/>\r\ntitle = {Low Overhead Parallel Schedules for Task Graphs},<br \/>\r\nauthor = {Richard J. Anderson and Paul Beame and Walter L. Ruzzo},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/1401.1872},<br \/>\r\nyear  = {1990},<br \/>\r\ndate = {1990-06-01},<br \/>\r\nbooktitle = {Proceedings of the 1990 ACM Symposium on Parallel Algorithms and Architectures},<br \/>\r\npages = {66-75},<br \/>\r\naddress = {Crete, Greece},<br \/>\r\nabstract = {Introduces a task scheduling model which is useful in the design and analysis of algorithms for small parallel machines. The authors prove that under their model, the overhead experienced in scheduling an n*n grid graph is O(log log n) for p processors, p&gt;or=2. They also prove a matching lower bound of Omega (log logn) for p processors, p&gt;or=2. They give an extension of the model to cover the case where the processors can have varying speed or are subject to delay.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('8','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_8\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Introduces a task scheduling model which is useful in the design and analysis of algorithms for small parallel machines. The authors prove that under their model, the overhead experienced in scheduling an n*n grid graph is O(log log n) for p processors, p&gt;or=2. They also prove a matching lower bound of Omega (log logn) for p processors, p&gt;or=2. They give an extension of the model to cover the case where the processors can have varying speed or are subject to delay.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('8','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_8\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/1401.1872\" title=\"https:\/\/arxiv.org\/abs\/1401.1872\" target=\"_blank\">https:\/\/arxiv.org\/abs\/1401.1872<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('8','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('18','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Recognizing Small Cliques on CRCW PRAM's<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Discrete Applied Mathematics, <\/span><span class=\"tp_pub_additional_volume\">vol. 29, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 3-20, <\/span><span class=\"tp_pub_additional_year\">1990<\/span><span class=\"tp_pub_additional_note\">, (Special issue on the applications of combinatorics to parallel \r\n\tcomputation)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_18\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('18','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_18\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bea90,<br \/>\r\ntitle = {Lower Bounds for Recognizing Small Cliques on CRCW PRAM's},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf},<br \/>\r\nyear  = {1990},<br \/>\r\ndate = {1990-01-01},<br \/>\r\njournal = {Discrete Applied Mathematics},<br \/>\r\nvolume = {29},<br \/>\r\nnumber = {1},<br \/>\r\npages = {3-20},<br \/>\r\nnote = {Special issue on the applications of combinatorics to parallel <br \/>\r\n\tcomputation},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('18','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_18\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('18','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Luby, Michael<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('111','tp_links')\" style=\"cursor:pointer;\">Parallel Search for Maximal Independence Given Minimal Dependence<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, <\/span><span class=\"tp_pub_additional_pages\">pp. 212-218, <\/span><span class=\"tp_pub_additional_organization\">ACM <\/span><span class=\"tp_pub_additional_address\">San Francisco, CA, <\/span><span class=\"tp_pub_additional_year\">1990<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_111\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('111','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_111\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bl:mish,<br \/>\r\ntitle = {Parallel Search for Maximal Independence Given Minimal Dependence},<br \/>\r\nauthor = {Paul Beame and Michael Luby},<br \/>\r\nurl = {https:\/\/dl.acm.org\/doi\/10.5555\/320176.320200},<br \/>\r\nyear  = {1990},<br \/>\r\ndate = {1990-01-01},<br \/>\r\nurldate = {1990-01-01},<br \/>\r\nbooktitle = {Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms},<br \/>\r\npages = {212-218},<br \/>\r\naddress = {San Francisco, CA},<br \/>\r\norganization = {ACM},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('111','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_111\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dl.acm.org\/doi\/10.5555\/320176.320200\" title=\"https:\/\/dl.acm.org\/doi\/10.5555\/320176.320200\" target=\"_blank\">https:\/\/dl.acm.org\/doi\/10.5555\/320176.320200<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('111','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Bodlaender, Hans<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('28','tp_links')\" style=\"cursor:pointer;\">Distributed Computing on Transitive Networks: The Torus<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">STACS 89: 6th Annual Symposium on Theoretical Aspects of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 294-303, <\/span><span class=\"tp_pub_additional_publisher\">Springer-Verlag, <\/span><span class=\"tp_pub_additional_address\">Bordeaux, France, <\/span><span class=\"tp_pub_additional_year\">1989<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_28\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('28','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_28\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bb:torus,<br \/>\r\ntitle = {Distributed Computing on Transitive Networks: The Torus},<br \/>\r\nauthor = {Paul Beame and Hans Bodlaender},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/grid.ps <br \/>\r\nhttp:\/\/link.springer.com\/chapter\/10.1007%2FBFb0028993},<br \/>\r\nyear  = {1989},<br \/>\r\ndate = {1989-02-01},<br \/>\r\nurldate = {1989-01-01},<br \/>\r\nbooktitle = {STACS 89: 6th Annual Symposium on Theoretical Aspects of Computer Science},<br \/>\r\nvolume = {349},<br \/>\r\npages = {294-303},<br \/>\r\npublisher = {Springer-Verlag},<br \/>\r\naddress = {Bordeaux, France},<br \/>\r\nseries = {Lecture Notes in Computer Science},<br \/>\r\ncrossref = {stacs89},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('28','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_28\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/grid.ps\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/grid.ps\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/grid.ps<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/link.springer.com\/chapter\/10.1007%2FBFb0028993\" title=\"http:\/\/link.springer.com\/chapter\/10.1007%2FBFb0028993\" target=\"_blank\">http:\/\/link.springer.com\/chapter\/10.1007%2FBFb0028993<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('28','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('14','tp_links')\" style=\"cursor:pointer;\">Limits on the Power of Concurrent-Write Parallel Machines<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Information and Computation, <\/span><span class=\"tp_pub_additional_volume\">vol. 76, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 13-28, <\/span><span class=\"tp_pub_additional_year\">1988<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_14\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('14','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_14\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bea88,<br \/>\r\ntitle = {Limits on the Power of Concurrent-Write Parallel Machines},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf},<br \/>\r\nyear  = {1988},<br \/>\r\ndate = {1988-01-01},<br \/>\r\njournal = {Information and Computation},<br \/>\r\nvolume = {76},<br \/>\r\nnumber = {1},<br \/>\r\npages = {13-28},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('14','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_14\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('14','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul W.;  Cook, Stephen A.;  Hoover, H. James<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('48','tp_links')\" style=\"cursor:pointer;\">Log Depth Circuits for Division and Related Problems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 15, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 994-1003, <\/span><span class=\"tp_pub_additional_year\">1986<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_48\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('48','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_48\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bch86,<br \/>\r\ntitle = {Log Depth Circuits for Division and Related Problems},<br \/>\r\nauthor = {Paul W. Beame and Stephen A. Cook and H. James Hoover},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/division.pdf},<br \/>\r\nyear  = {1986},<br \/>\r\ndate = {1986-11-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {15},<br \/>\r\nnumber = {4},<br \/>\r\npages = {994-1003},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('48','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_48\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/division.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/division.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/division.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('48','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_phdthesis\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul W.<\/p><p class=\"tp_pub_title\">Lower Bounds in Parallel Machine Computation <span class=\"tp_pub_type tp_  phdthesis\">PhD Thesis<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_school\">University of Toronto, <\/span><span class=\"tp_pub_additional_year\">1986<\/span><span class=\"tp_pub_additional_note\">, (Department of Computer Science Technical Report 198\/87)<\/span>.<\/p><p class=\"tp_pub_menu\"><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_13\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@phdthesis{bea86:thesis,<br \/>\r\ntitle = {Lower Bounds in Parallel Machine Computation},<br \/>\r\nauthor = {Paul W. Beame},<br \/>\r\nyear  = {1986},<br \/>\r\ndate = {1986-01-01},<br \/>\r\nschool = {University of Toronto},<br \/>\r\nnote = {Department of Computer Science Technical Report 198\/87},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {phdthesis}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('13','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul W.;  Cook, Stephen A.;  Hoover, H. James<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('46','tp_links')\" style=\"cursor:pointer;\">Log Depth Circuits for Division and Related Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">25th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 1-6, <\/span><span class=\"tp_pub_additional_publisher\">IEEE, <\/span><span class=\"tp_pub_additional_address\">Singer Island, FL, <\/span><span class=\"tp_pub_additional_year\">1984<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_46\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('46','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_46\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bch84,<br \/>\r\ntitle = {Log Depth Circuits for Division and Related Problems},<br \/>\r\nauthor = {Paul W. Beame and Stephen A. Cook and H. James Hoover},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsdivision.pdf},<br \/>\r\nyear  = {1984},<br \/>\r\ndate = {1984-11-01},<br \/>\r\nbooktitle = {25th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {1-6},<br \/>\r\npublisher = {IEEE},<br \/>\r\naddress = {Singer Island, FL},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('46','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_46\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsdivision.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsdivision.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsdivision.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('46','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_mastersthesis\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul W.<\/p><p class=\"tp_pub_title\">Random Routing in Constant Degree Networks <span class=\"tp_pub_type tp_  mastersthesis\">Masters Thesis<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_school\">Department of Computer Science, University of Toronto, <\/span><span class=\"tp_pub_additional_year\">1982<\/span><span class=\"tp_pub_additional_note\">, (Technical Report 161\/82)<\/span>.<\/p><p class=\"tp_pub_menu\"><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_11\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@mastersthesis{bea82,<br \/>\r\ntitle = {Random Routing in Constant Degree Networks},<br \/>\r\nauthor = {Paul W. Beame},<br \/>\r\nyear  = {1982},<br \/>\r\ndate = {1982-01-01},<br \/>\r\nschool = {Department of Computer Science, University of Toronto},<br \/>\r\nnote = {Technical Report 161\/82},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {mastersthesis}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('11','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-data\"><strong>Data Structures<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Fich, Faith<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('147','tp_links')\" style=\"cursor:pointer;\">Optimal Bounds for the Predecessor Problem and Related Problems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Computer and System Sciences, <\/span><span class=\"tp_pub_additional_volume\">vol. 65, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 38\u201372, <\/span><span class=\"tp_pub_additional_year\">2002<\/span><span class=\"tp_pub_additional_note\">, (Special issue of selected papers from 1999 STOC conference.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_147\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('147','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_147\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bf:pred-journal,<br \/>\r\ntitle = {Optimal Bounds for the Predecessor Problem and Related Problems},<br \/>\r\nauthor = {Paul Beame and Faith Fich},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/predecessor.pdf},<br \/>\r\nyear  = {2002},<br \/>\r\ndate = {2002-08-01},<br \/>\r\njournal = {Journal of Computer and System Sciences},<br \/>\r\nvolume = {65},<br \/>\r\nnumber = {1},<br \/>\r\npages = {38\u201372},<br \/>\r\nnote = {Special issue of selected papers from 1999 STOC conference.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('147','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_147\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/predecessor.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/predecessor.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/predecessor.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('147','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Vee, Erik<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('165','tp_links')\" style=\"cursor:pointer;\">Time-Space Tradeoffs, Multiparty Communication \r\n Complexity, and Nearest-Neighbor Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 688-697, <\/span><span class=\"tp_pub_additional_address\">Montreal, Quebec, Canada, <\/span><span class=\"tp_pub_additional_year\">2002<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_165\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('165','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_165\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bv:multibp,<br \/>\r\ntitle = {Time-Space Tradeoffs, Multiparty Communication <br \/>\r\n Complexity, and Nearest-Neighbor Problems},<br \/>\r\nauthor = {Paul Beame and Erik Vee},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf},<br \/>\r\nyear  = {2002},<br \/>\r\ndate = {2002-05-01},<br \/>\r\nurldate = {2002-05-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {688-697},<br \/>\r\naddress = {Montreal, Quebec, Canada},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('165','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_165\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multibp.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('165','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Fich, Faith<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('145','tp_links')\" style=\"cursor:pointer;\">Optimal Bounds for the Predecessor Problem<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 295\u2013304, <\/span><span class=\"tp_pub_additional_address\">Atlanta, GA, <\/span><span class=\"tp_pub_additional_year\">1999<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_145\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('145','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_145\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bf:pred,<br \/>\r\ntitle = {Optimal Bounds for the Predecessor Problem},<br \/>\r\nauthor = {Paul Beame and Faith Fich},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocpred.pdf},<br \/>\r\nyear  = {1999},<br \/>\r\ndate = {1999-05-01},<br \/>\r\nurldate = {1999-05-01},<br \/>\r\nbooktitle = {Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {295\u2013304},<br \/>\r\naddress = {Atlanta, GA},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('145','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_145\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocpred.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocpred.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocpred.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('145','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Fich, Faith<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('144','tp_links')\" style=\"cursor:pointer;\">On Searching Sorted Lists: A Near-Optimal Lower Bound<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Department of Computer Science and Engineering, University of Washington <\/span><span class=\"tp_pub_additional_number\">no. UW-CSE-97-09-02, <\/span><span class=\"tp_pub_additional_year\">1997<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_144\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('144','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_144\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bf:search-tr,<br \/>\r\ntitle = {On Searching Sorted Lists: A Near-Optimal Lower Bound},<br \/>\r\nauthor = {Paul Beame and Faith Fich},<br \/>\r\nurl = {https:\/\/dada.cs.washington.edu\/research\/tr\/1997\/09\/UW-CSE-97-09-02.pdf},<br \/>\r\nyear  = {1997},<br \/>\r\ndate = {1997-04-01},<br \/>\r\nurldate = {1997-04-01},<br \/>\r\nnumber = {UW-CSE-97-09-02},<br \/>\r\ninstitution = {Department of Computer Science and Engineering, University of Washington},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('144','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_144\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dada.cs.washington.edu\/research\/tr\/1997\/09\/UW-CSE-97-09-02.pdf\" title=\"https:\/\/dada.cs.washington.edu\/research\/tr\/1997\/09\/UW-CSE-97-09-02.pdf\" target=\"_blank\">https:\/\/dada.cs.washington.edu\/research\/tr\/1997\/09\/UW-CSE-97-09-02.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('144','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-circuit\"><strong>Circuit and PRAM Lower Bounds<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Grosshans, Nathan;  McKenzie, Pierre;  Segoufin, Luc<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('55','tp_links')\" style=\"cursor:pointer;\">Nondeterminism and an abstract formulation of Ne\u010diporuk's lower bound method<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1608.01932, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_55\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('55','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_55\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bgms:neciporuk-tr,<br \/>\r\ntitle = {Nondeterminism and an abstract formulation of Ne\u010diporuk's lower bound method},<br \/>\r\nauthor = {Paul Beame and Nathan Grosshans and Pierre McKenzie and Luc Segoufin},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1608.01932},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-08-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1608.01932},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('55','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_55\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1608.01932\" title=\"http:\/\/arxiv.org\/abs\/1608.01932\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1608.01932<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('55','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Grosshans, Nathan;  McKenzie, Pierre;  Segoufin, Luc<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('56','tp_links')\" style=\"cursor:pointer;\">Nondeterminism and an Abstract Formulation of Ne\u010diporuk's Lower Bound Method<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">ACM Transactions on Computation Theory, <\/span><span class=\"tp_pub_additional_volume\">vol. 9, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 5:1\u20135:34, <\/span><span class=\"tp_pub_additional_year\">2016<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_56\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('56','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_56\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bgms:neciporuk,<br \/>\r\ntitle = {Nondeterminism and an Abstract Formulation of Ne\u010diporuk's Lower Bound Method},<br \/>\r\nauthor = {Paul Beame and Nathan Grosshans and Pierre McKenzie and Luc Segoufin},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/neciporuk.pdf},<br \/>\r\nyear  = {2016},<br \/>\r\ndate = {2016-01-01},<br \/>\r\nurldate = {2016-01-01},<br \/>\r\njournal = {ACM Transactions on Computation Theory},<br \/>\r\nvolume = {9},<br \/>\r\nnumber = {1},<br \/>\r\npages = {5:1\u20135:34},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('56','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_56\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/neciporuk.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/neciporuk.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/neciporuk.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('56','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Srinivasan, Srikanth<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('78','tp_links')\" style=\"cursor:pointer;\">Approximating $AC^0$ Circuits by Small Height Decision Trees \r\n and a Deterministic Algorithm for $#AC^0$-SAT<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings Twenty-Seventh Annual IEEE Conference on Computational Complexity, <\/span><span class=\"tp_pub_additional_pages\">pp. 117\u2013125, <\/span><span class=\"tp_pub_additional_address\">Porto, Portugal, <\/span><span class=\"tp_pub_additional_year\">2012<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_78\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('78','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_78\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bis:parity,<br \/>\r\ntitle = {Approximating $AC^0$ Circuits by Small Height Decision Trees <br \/>\r\n and a Deterministic Algorithm for $#AC^0$-SAT},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Srikanth Srinivasan},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ac0approx.pdf},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-06-01},<br \/>\r\nbooktitle = {Proceedings Twenty-Seventh Annual IEEE Conference on Computational Complexity},<br \/>\r\npages = {117\u2013125},<br \/>\r\naddress = {Porto, Portugal},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('78','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_78\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ac0approx.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ac0approx.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/ac0approx.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('78','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh, Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('65','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Computing, <\/span><span class=\"tp_pub_additional_volume\">vol. 41, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 484\u2013518, <\/span><span class=\"tp_pub_additional_year\">2012<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_65\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('65','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_65\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bh:multiparty-journal,<br \/>\r\ntitle = {Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Trinh Huynh},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-01-01},<br \/>\r\njournal = {SIAM Journal on Computing},<br \/>\r\nvolume = {41},<br \/>\r\nnumber = {3},<br \/>\r\npages = {484\u2013518},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('65','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_65\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0j.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('65','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('114','tp_links')\" style=\"cursor:pointer;\">The Quantum Query Complexity of $AC^0$<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Quantum Information &amp; Computation, <\/span><span class=\"tp_pub_additional_volume\">vol. 12, <\/span><span class=\"tp_pub_additional_number\">no. 7\u20138, <\/span><span class=\"tp_pub_additional_pages\">pp. 670\u2013676, <\/span><span class=\"tp_pub_additional_year\">2012<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_114\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('114','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_114\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bm:qac0,<br \/>\r\ntitle = {The Quantum Query Complexity of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-01-01},<br \/>\r\nurldate = {2012-01-01},<br \/>\r\njournal = {Quantum Information & Computation},<br \/>\r\nvolume = {12},<br \/>\r\nnumber = {7\u20138},<br \/>\r\npages = {670\u2013676},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('114','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_114\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('114','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('113','tp_links')\" style=\"cursor:pointer;\">The Quantum Query Complexity of $AC^0$<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">arxiv\/quant-phys <\/span><span class=\"tp_pub_additional_number\">no. arXiv:1008.2422v1, <\/span><span class=\"tp_pub_additional_year\">2010<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_113\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('113','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_113\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bm:qac0-arxiv,<br \/>\r\ntitle = {The Quantum Query Complexity of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1008.2422},<br \/>\r\nyear  = {2010},<br \/>\r\ndate = {2010-01-01},<br \/>\r\nnumber = {arXiv:1008.2422v1},<br \/>\r\ninstitution = {arxiv\/quant-phys},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('113','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_113\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1008.2422\" title=\"http:\/\/arxiv.org\/abs\/1008.2422\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1008.2422<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('113','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh-Ngoc, Dang-Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('64','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 50th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 53\u201362, <\/span><span class=\"tp_pub_additional_organization\">IEEE <\/span><span class=\"tp_pub_additional_address\">Atlanta, GA, <\/span><span class=\"tp_pub_additional_year\">2009<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_64\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('64','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_64\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bh-n:multiparty,<br \/>\r\ntitle = {Multiparty Communication Complexity and Threshold Circuit Size of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Dang-Trinh Huynh-Ngoc},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf},<br \/>\r\nyear  = {2009},<br \/>\r\ndate = {2009-10-01},<br \/>\r\nurldate = {2009-10-01},<br \/>\r\nbooktitle = {Proceedings 50th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {53\u201362},<br \/>\r\naddress = {Atlanta, GA},<br \/>\r\norganization = {IEEE},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('64','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_64\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsmultiac0.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('64','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Huynh-Ngoc, Dang-Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('63','tp_links')\" style=\"cursor:pointer;\">Multiparty Communication Complexity and Threshold Circuit Complexity of $AC^0$<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Electronic Colloquium on Computational Complexity <\/span><span class=\"tp_pub_additional_number\">no. TR08-082, <\/span><span class=\"tp_pub_additional_year\">2008<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_63\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('63','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_63\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bh-n:multiparty-eccc,<br \/>\r\ntitle = {Multiparty Communication Complexity and Threshold Circuit Complexity of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Dang-Trinh Huynh-Ngoc},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf},<br \/>\r\nyear  = {2008},<br \/>\r\ndate = {2008-01-01},<br \/>\r\nnumber = {TR08-082},<br \/>\r\ninstitution = {Electronic Colloquium on Computational Complexity},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('63','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_63\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/multiac0.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('63','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('72','tp_links')\" style=\"cursor:pointer;\">Improved Depth Bounds for Small Distance Connectivity<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Computational Complexity, <\/span><span class=\"tp_pub_additional_volume\">vol. 7, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 325\u2013345, <\/span><span class=\"tp_pub_additional_year\">1998<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_72\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('72','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_72\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bip:smallconn-journal,<br \/>\r\ntitle = {Improved Depth Bounds for Small Distance Connectivity},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stconn-journal.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-01-01},<br \/>\r\njournal = {Computational Complexity},<br \/>\r\nvolume = {7},<br \/>\r\nnumber = {4},<br \/>\r\npages = {325\u2013345},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('72','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_72\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stconn-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stconn-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stconn-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('72','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Fich, Faith E.;  Sinha, Rakesh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('54','tp_links')\" style=\"cursor:pointer;\">Separating the Power of EREW and CREW PRAMs with Small Communication Width<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Information and Computation, <\/span><span class=\"tp_pub_additional_volume\">vol. 138, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 89-99, <\/span><span class=\"tp_pub_additional_year\">1997<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_54\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('54','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_54\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bfs:erew-journal,<br \/>\r\ntitle = {Separating the Power of EREW and CREW PRAMs with Small Communication Width},<br \/>\r\nauthor = {Paul Beame and Faith E. Fich and Rakesh Sinha},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew-journal.pdf},<br \/>\r\nyear  = {1997},<br \/>\r\ndate = {1997-10-01},<br \/>\r\nurldate = {1997-10-01},<br \/>\r\njournal = {Information and Computation},<br \/>\r\nvolume = {138},<br \/>\r\nnumber = {1},<br \/>\r\npages = {89-99},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('54','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_54\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew-journal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew-journal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew-journal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('54','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Impagliazzo, Russell;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('71','tp_links')\" style=\"cursor:pointer;\">Improved Depth Bounds for Small Distance Connectivity<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings 36th Annual Symposium on Foundations of Computer Science, <\/span><span class=\"tp_pub_additional_pages\">pp. 692-701, <\/span><span class=\"tp_pub_additional_publisher\">IEEE, <\/span><span class=\"tp_pub_additional_address\">Milwaukee, WI, <\/span><span class=\"tp_pub_additional_year\">1995<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_71\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('71','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_71\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bip:smallconn,<br \/>\r\ntitle = {Improved Depth Bounds for Small Distance Connectivity},<br \/>\r\nauthor = {Paul Beame and Russell Impagliazzo and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsconn.pdf},<br \/>\r\nyear  = {1995},<br \/>\r\ndate = {1995-10-01},<br \/>\r\nbooktitle = {Proceedings 36th Annual Symposium on Foundations of Computer Science},<br \/>\r\npages = {692-701},<br \/>\r\npublisher = {IEEE},<br \/>\r\naddress = {Milwaukee, WI},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('71','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_71\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsconn.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsconn.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/focsconn.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('71','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('20','tp_links')\" style=\"cursor:pointer;\">A Switching Lemma Primer<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">Department of Computer Science and Engineering, University of Washington <\/span><span class=\"tp_pub_additional_number\">no. UW-CSE-95\u201307\u201301, <\/span><span class=\"tp_pub_additional_year\">1994<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_20\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('20','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_20\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{beame:primer,<br \/>\r\ntitle = {A Switching Lemma Primer},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/primer.ps},<br \/>\r\nyear  = {1994},<br \/>\r\ndate = {1994-11-01},<br \/>\r\nnumber = {UW-CSE-95\u201307\u201301},<br \/>\r\ninstitution = {Department of Computer Science and Engineering, University of Washington},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('20','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_20\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/primer.ps\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/primer.ps\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/primer.ps<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('20','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Fich, Faith E.;  Sinha, Rakesh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('53','tp_links')\" style=\"cursor:pointer;\">Separating the Power of EREW and CREW PRAMs with Small Communication Width<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 1993 Workshop on Algorithms and Data Structures, <\/span><span class=\"tp_pub_additional_pages\">pp. 163-174, <\/span><span class=\"tp_pub_additional_year\">1993<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_53\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('53','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_53\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bfs:erew,<br \/>\r\ntitle = {Separating the Power of EREW and CREW PRAMs with Small Communication Width},<br \/>\r\nauthor = {Paul Beame and Faith E. Fich and Rakesh Sinha},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew.ps <br \/>\r\nhttp:\/\/link.springer.com\/chapter\/10.1007%2F3-540-57155-8_245},<br \/>\r\nyear  = {1993},<br \/>\r\ndate = {1993-01-01},<br \/>\r\nbooktitle = {Proceedings of the 1993 Workshop on Algorithms and Data Structures},<br \/>\r\npages = {163-174},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('53','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_53\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew.ps\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew.ps\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crew.ps<\/a><\/li><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/link.springer.com\/chapter\/10.1007%2F3-540-57155-8_245\" title=\"http:\/\/link.springer.com\/chapter\/10.1007%2F3-540-57155-8_245\" target=\"_blank\">http:\/\/link.springer.com\/chapter\/10.1007%2F3-540-57155-8_245<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('53','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Brisson, Eric;  Ladner, Richard E.<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('36','tp_links')\" style=\"cursor:pointer;\">The Complexity of Computing Symmetric Functions using Threshold Circuits<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Theoretical Computer Science, <\/span><span class=\"tp_pub_additional_volume\">vol. 100, <\/span><span class=\"tp_pub_additional_pages\">pp. 253-265, <\/span><span class=\"tp_pub_additional_year\">1992<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_36\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('36','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_36\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bbl92,<br \/>\r\ntitle = {The Complexity of Computing Symmetric Functions using Threshold Circuits},<br \/>\r\nauthor = {Paul Beame and Eric Brisson and Richard E. Ladner},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf},<br \/>\r\nyear  = {1992},<br \/>\r\ndate = {1992-01-01},<br \/>\r\njournal = {Theoretical Computer Science},<br \/>\r\nvolume = {100},<br \/>\r\npages = {253-265},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('36','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_36\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/symm.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('36','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('18','tp_links')\" style=\"cursor:pointer;\">Lower Bounds for Recognizing Small Cliques on CRCW PRAM's<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Discrete Applied Mathematics, <\/span><span class=\"tp_pub_additional_volume\">vol. 29, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 3-20, <\/span><span class=\"tp_pub_additional_year\">1990<\/span><span class=\"tp_pub_additional_note\">, (Special issue on the applications of combinatorics to parallel \r\n\tcomputation)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_18\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('18','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_18\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bea90,<br \/>\r\ntitle = {Lower Bounds for Recognizing Small Cliques on CRCW PRAM's},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf},<br \/>\r\nyear  = {1990},<br \/>\r\ndate = {1990-01-01},<br \/>\r\njournal = {Discrete Applied Mathematics},<br \/>\r\nvolume = {29},<br \/>\r\nnumber = {1},<br \/>\r\npages = {3-20},<br \/>\r\nnote = {Special issue on the applications of combinatorics to parallel <br \/>\r\n\tcomputation},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('18','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_18\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/clique.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('18','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  H\u00e5stad, Johan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('58','tp_links')\" style=\"cursor:pointer;\">Optimal Bounds for Decision Problems on the CRCW PRAM<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of the ACM, <\/span><span class=\"tp_pub_additional_volume\">vol. 36, <\/span><span class=\"tp_pub_additional_number\">no. 3, <\/span><span class=\"tp_pub_additional_pages\">pp. 643-670, <\/span><span class=\"tp_pub_additional_year\">1989<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_58\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('58','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_58\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bh:crcw,<br \/>\r\ntitle = {Optimal Bounds for Decision Problems on the CRCW PRAM},<br \/>\r\nauthor = {Paul Beame and Johan H\u00e5stad},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crcwparity.pdf},<br \/>\r\nyear  = {1989},<br \/>\r\ndate = {1989-07-01},<br \/>\r\njournal = {Journal of the ACM},<br \/>\r\nvolume = {36},<br \/>\r\nnumber = {3},<br \/>\r\npages = {643-670},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('58','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_58\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crcwparity.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crcwparity.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/crcwparity.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('58','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('14','tp_links')\" style=\"cursor:pointer;\">Limits on the Power of Concurrent-Write Parallel Machines<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Information and Computation, <\/span><span class=\"tp_pub_additional_volume\">vol. 76, <\/span><span class=\"tp_pub_additional_number\">no. 1, <\/span><span class=\"tp_pub_additional_pages\">pp. 13-28, <\/span><span class=\"tp_pub_additional_year\">1988<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_14\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('14','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_14\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bea88,<br \/>\r\ntitle = {Limits on the Power of Concurrent-Write Parallel Machines},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf},<br \/>\r\nyear  = {1988},<br \/>\r\ndate = {1988-01-01},<br \/>\r\njournal = {Information and Computation},<br \/>\r\nvolume = {76},<br \/>\r\nnumber = {1},<br \/>\r\npages = {13-28},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('14','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_14\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/limits.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('14','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  H\u00e5stad, Johan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('57','tp_links')\" style=\"cursor:pointer;\">Optimal Bounds for Decision Problems on the CRCW PRAM<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 83-93, <\/span><span class=\"tp_pub_additional_address\">New York, NY, <\/span><span class=\"tp_pub_additional_year\">1987<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_57\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('57','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_57\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bh87,<br \/>\r\ntitle = {Optimal Bounds for Decision Problems on the CRCW PRAM},<br \/>\r\nauthor = {Paul Beame and Johan H\u00e5stad},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoccrcw.pdf},<br \/>\r\nyear  = {1987},<br \/>\r\ndate = {1987-05-01},<br \/>\r\nbooktitle = {Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {83-93},<br \/>\r\naddress = {New York, NY},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('57','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_57\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoccrcw.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoccrcw.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoccrcw.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('57','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('12','tp_links')\" style=\"cursor:pointer;\">Limits on the Power of Concurrent-Write Parallel Machines<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 169-176, <\/span><span class=\"tp_pub_additional_address\">Berkeley, CA, <\/span><span class=\"tp_pub_additional_year\">1986<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_12\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('12','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_12\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bea86,<br \/>\r\ntitle = {Limits on the Power of Concurrent-Write Parallel Machines},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoclimits.pdf},<br \/>\r\nyear  = {1986},<br \/>\r\ndate = {1986-05-01},<br \/>\r\nbooktitle = {Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {169-176},<br \/>\r\naddress = {Berkeley, CA},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('12','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_12\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoclimits.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoclimits.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stoclimits.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('12','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_phdthesis\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul W.<\/p><p class=\"tp_pub_title\">Lower Bounds in Parallel Machine Computation <span class=\"tp_pub_type tp_  phdthesis\">PhD Thesis<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_school\">University of Toronto, <\/span><span class=\"tp_pub_additional_year\">1986<\/span><span class=\"tp_pub_additional_note\">, (Department of Computer Science Technical Report 198\/87)<\/span>.<\/p><p class=\"tp_pub_menu\"><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_13\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@phdthesis{bea86:thesis,<br \/>\r\ntitle = {Lower Bounds in Parallel Machine Computation},<br \/>\r\nauthor = {Paul W. Beame},<br \/>\r\nyear  = {1986},<br \/>\r\ndate = {1986-01-01},<br \/>\r\nschool = {University of Toronto},<br \/>\r\nnote = {Department of Computer Science Technical Report 198\/87},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {phdthesis}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('13','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beame-other\"><strong>Other Topics<\/strong><\/h3>\n\n\n<div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Har-Peled, Sariel;  Ramamoorthy, Sivaramakrishnan Natarajan;  Rashtchian, Cyrus;  Sinha, Makrand<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('152','tp_links')\" style=\"cursor:pointer;\">Edge Estimation with Independent Set Oracles<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">ACM Transactions on Algorithms, <\/span><span class=\"tp_pub_additional_volume\">vol. 16, <\/span><span class=\"tp_pub_additional_number\">no. 4, <\/span><span class=\"tp_pub_additional_pages\">pp. 52:1-52:27, <\/span><span class=\"tp_pub_additional_year\">2020<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_152\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('152','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_152\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bhpnrrs:is-oracle-journal,<br \/>\r\ntitle = {Edge Estimation with Independent Set Oracles},<br \/>\r\nauthor = {Paul Beame and Sariel Har-Peled and Sivaramakrishnan Natarajan Ramamoorthy and Cyrus Rashtchian and Makrand Sinha},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/edge_est.pdf},<br \/>\r\nyear  = {2020},<br \/>\r\ndate = {2020-09-01},<br \/>\r\njournal = {ACM Transactions on Algorithms},<br \/>\r\nvolume = {16},<br \/>\r\nnumber = {4},<br \/>\r\npages = {52:1-52:27},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('152','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_152\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/edge_est.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/edge_est.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/edge_est.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('152','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('23','tp_links')\" style=\"cursor:pointer;\">Technical perspective: Two for the price of one<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Communications of the ACM, <\/span><span class=\"tp_pub_additional_volume\">vol. 63, <\/span><span class=\"tp_pub_additional_number\">no. 10, <\/span><span class=\"tp_pub_additional_pages\">pp. 96, <\/span><span class=\"tp_pub_additional_year\">2020<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_23\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('23','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_23\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{beame:cacm-perspective,<br \/>\r\ntitle = {Technical perspective: Two for the price of one},<br \/>\r\nauthor = {Paul Beame},<br \/>\r\nurl = {https:\/\/doi.org\/10.1145\/3416264},<br \/>\r\ndoi = {10.1145\/3416264},<br \/>\r\nyear  = {2020},<br \/>\r\ndate = {2020-01-01},<br \/>\r\njournal = {Communications of the ACM},<br \/>\r\nvolume = {63},<br \/>\r\nnumber = {10},<br \/>\r\npages = {96},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('23','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_23\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/doi.org\/10.1145\/3416264\" title=\"https:\/\/doi.org\/10.1145\/3416264\" target=\"_blank\">https:\/\/doi.org\/10.1145\/3416264<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1145\/3416264\" title=\"Follow DOI:10.1145\/3416264\" target=\"_blank\">doi:10.1145\/3416264<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('23','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Gharan, Shayan Oveis;  Yang, Xin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('157','tp_links')\" style=\"cursor:pointer;\">On the Bias of Reed-Muller Codes over Odd Prime Fields<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">SIAM Journal on Discrete Mathematics, <\/span><span class=\"tp_pub_additional_volume\">vol. 34, <\/span><span class=\"tp_pub_additional_number\">no. 2, <\/span><span class=\"tp_pub_additional_pages\">pp. 1232\u20131247, <\/span><span class=\"tp_pub_additional_year\">2020<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_157\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('157','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_157\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bogy:polybias,<br \/>\r\ntitle = {On the Bias of Reed-Muller Codes over Odd Prime Fields},<br \/>\r\nauthor = {Paul Beame and Shayan Oveis Gharan and Xin Yang},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/polybias.pdf},<br \/>\r\nyear  = {2020},<br \/>\r\ndate = {2020-01-01},<br \/>\r\njournal = {SIAM Journal on Discrete Mathematics},<br \/>\r\nvolume = {34},<br \/>\r\nnumber = {2},<br \/>\r\npages = {1232\u20131247},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('157','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_157\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/polybias.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/polybias.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/polybias.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('157','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Har-Peled, Sariel;  Ramamoorthy, Sivaramakrishnan Natarajan;  Rashtchian, Cyrus;  Sinha, Makrand<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('151','tp_links')\" style=\"cursor:pointer;\">Edge Estimation with Independent Set Oracles<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the 9th Innovations in Theoretical \r\n Computer Science Conference (ITCS 2018), <\/span><span class=\"tp_pub_additional_pages\">pp. 38:1\u201338:21, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_151\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('151','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_151\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bhpnrrs:is-oracle,<br \/>\r\ntitle = {Edge Estimation with Independent Set Oracles},<br \/>\r\nauthor = {Paul Beame and Sariel Har-Peled and Sivaramakrishnan Natarajan Ramamoorthy and Cyrus Rashtchian and Makrand Sinha},<br \/>\r\nurl = {http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8355},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-01-01},<br \/>\r\nbooktitle = {Proceedings of the 9th Innovations in Theoretical <br \/>\r\n Computer Science Conference (ITCS 2018)},<br \/>\r\nvolume = {94},<br \/>\r\npages = {38:1\u201338:21},<br \/>\r\nseries = {Leibniz International Proceedings in Informatics (LIPIcs)},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('151','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_151\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8355\" title=\"http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8355\" target=\"_blank\">http:\/\/drops.dagstuhl.de\/opus\/volltexte\/2018\/8355<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('151','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Gharan, Shayan Oveis;  Yang, Xin<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('156','tp_links')\" style=\"cursor:pointer;\">On the Bias of Reed-Muller Codes over Odd Prime Fields<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">CoRR, <\/span><span class=\"tp_pub_additional_volume\">vol. abs\/1806.06973, <\/span><span class=\"tp_pub_additional_year\">2018<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_156\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('156','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_156\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bogy:polybias-tr,<br \/>\r\ntitle = {On the Bias of Reed-Muller Codes over Odd Prime Fields},<br \/>\r\nauthor = {Paul Beame and Shayan Oveis Gharan and Xin Yang},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1806.06973},<br \/>\r\nyear  = {2018},<br \/>\r\ndate = {2018-01-01},<br \/>\r\njournal = {CoRR},<br \/>\r\nvolume = {abs\/1806.06973},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('156','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_156\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1806.06973\" title=\"http:\/\/arxiv.org\/abs\/1806.06973\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1806.06973<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('156','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('114','tp_links')\" style=\"cursor:pointer;\">The Quantum Query Complexity of $AC^0$<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Quantum Information &amp; Computation, <\/span><span class=\"tp_pub_additional_volume\">vol. 12, <\/span><span class=\"tp_pub_additional_number\">no. 7\u20138, <\/span><span class=\"tp_pub_additional_pages\">pp. 670\u2013676, <\/span><span class=\"tp_pub_additional_year\">2012<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_114\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('114','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_114\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bm:qac0,<br \/>\r\ntitle = {The Quantum Query Complexity of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf},<br \/>\r\nyear  = {2012},<br \/>\r\ndate = {2012-01-01},<br \/>\r\nurldate = {2012-01-01},<br \/>\r\njournal = {Quantum Information & Computation},<br \/>\r\nvolume = {12},<br \/>\r\nnumber = {7\u20138},<br \/>\r\npages = {670\u2013676},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('114','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_114\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/qac0-QIC.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('114','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Machmouchi, Widad<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('113','tp_links')\" style=\"cursor:pointer;\">The Quantum Query Complexity of $AC^0$<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">arxiv\/quant-phys <\/span><span class=\"tp_pub_additional_number\">no. arXiv:1008.2422v1, <\/span><span class=\"tp_pub_additional_year\">2010<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_113\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('113','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_113\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bm:qac0-arxiv,<br \/>\r\ntitle = {The Quantum Query Complexity of $AC^0$},<br \/>\r\nauthor = {Paul Beame and Widad Machmouchi},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/1008.2422},<br \/>\r\nyear  = {2010},<br \/>\r\ndate = {2010-01-01},<br \/>\r\nnumber = {arXiv:1008.2422v1},<br \/>\r\ninstitution = {arxiv\/quant-phys},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('113','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_113\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/1008.2422\" title=\"http:\/\/arxiv.org\/abs\/1008.2422\" target=\"_blank\">http:\/\/arxiv.org\/abs\/1008.2422<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('113','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_techreport\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Blais, Eric;  Huynh-Ngoc, Dang-Trinh<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('27','tp_links')\" style=\"cursor:pointer;\">Longest Common Subsequences in Sets of Permutations<\/a> <span class=\"tp_pub_type tp_  techreport\">Technical Report<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_institution\">arxiv\/math.co <\/span><span class=\"tp_pub_additional_number\">no. arXiv:0904.1615, <\/span><span class=\"tp_pub_additional_year\">2009<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_27\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('27','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_27\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@techreport{bbh-n:permute-arxiv,<br \/>\r\ntitle = {Longest Common Subsequences in Sets of Permutations},<br \/>\r\nauthor = {Paul Beame and Eric Blais and Dang-Trinh Huynh-Ngoc},<br \/>\r\nurl = {http:\/\/arxiv.org\/abs\/0904.1615},<br \/>\r\nyear  = {2009},<br \/>\r\ndate = {2009-01-01},<br \/>\r\nnumber = {arXiv:0904.1615},<br \/>\r\ninstitution = {arxiv\/math.co},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {techreport}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('27','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_27\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/arxiv.org\/abs\/0904.1615\" title=\"http:\/\/arxiv.org\/abs\/0904.1615\" target=\"_blank\">http:\/\/arxiv.org\/abs\/0904.1615<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('27','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Cook, Stephen A.;  Edmonds, Jeff;  Impagliazzo, Russell;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('45','tp_links')\" style=\"cursor:pointer;\">The Relative Complexity of NP Search Problems<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">Journal of Computer and System Sciences, <\/span><span class=\"tp_pub_additional_volume\">vol. 57, <\/span><span class=\"tp_pub_additional_pages\">pp. 3\u201319, <\/span><span class=\"tp_pub_additional_year\">1998<\/span><span class=\"tp_pub_additional_note\">, (Special issue of invited papers from 1995 STOC conference.)<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_45\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('45','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_45\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{bceip:search-journal,<br \/>\r\ntitle = {The Relative Complexity of NP Search Problems},<br \/>\r\nauthor = {Paul Beame and Stephen A. Cook and Jeff Edmonds and Russell Impagliazzo and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf},<br \/>\r\nyear  = {1998},<br \/>\r\ndate = {1998-01-01},<br \/>\r\nurldate = {1998-01-01},<br \/>\r\njournal = {Journal of Computer and System Sciences},<br \/>\r\nvolume = {57},<br \/>\r\npages = {3\u201319},<br \/>\r\nnote = {Special issue of invited papers from 1995 STOC conference.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('45','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_45\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/NPSearchJournal.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('45','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Cook, Stephen A.;  Edmonds, Jeff;  Impagliazzo, Russell;  Pitassi, Toniann<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('44','tp_links')\" style=\"cursor:pointer;\">The Relative Complexity of NP Search Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, <\/span><span class=\"tp_pub_additional_pages\">pp. 303\u2013314, <\/span><span class=\"tp_pub_additional_address\">Las Vegas, NV, <\/span><span class=\"tp_pub_additional_year\">1995<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_44\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('44','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_44\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{bceip:search,<br \/>\r\ntitle = {The Relative Complexity of NP Search Problems},<br \/>\r\nauthor = {Paul Beame and Stephen A. Cook and Jeff Edmonds and Russell Impagliazzo and Toniann Pitassi},<br \/>\r\nurl = {http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf},<br \/>\r\nyear  = {1995},<br \/>\r\ndate = {1995-05-01},<br \/>\r\nbooktitle = {Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing},<br \/>\r\npages = {303\u2013314},<br \/>\r\naddress = {Las Vegas, NV},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('44','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_44\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-file-pdf\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf\" title=\"http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf\" target=\"_blank\">http:\/\/www.cs.washington.edu\/homes\/beame\/papers\/stocsearch.pdf<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('44','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_article\"><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Beame, Paul;  Muir, Paul<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('171','tp_links')\" style=\"cursor:pointer;\">On Error Expressions for Reflected and Averaged Implicit \r\n Runge-Kutta Methods<\/a> <span class=\"tp_pub_type tp_  article\">Journal Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_journal\">BIT, <\/span><span class=\"tp_pub_additional_volume\">vol. 29, <\/span><span class=\"tp_pub_additional_pages\">pp. 126-139, <\/span><span class=\"tp_pub_additional_year\">1989<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_resource_link\"><a id=\"tp_links_sh_171\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('171','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_171\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@article{mb:runge,<br \/>\r\ntitle = {On Error Expressions for Reflected and Averaged Implicit <br \/>\r\n Runge-Kutta Methods},<br \/>\r\nauthor = {Paul Beame and Paul Muir},<br \/>\r\ndoi = {10.1007\/BF01932710},<br \/>\r\nyear  = {1989},<br \/>\r\ndate = {1989-01-01},<br \/>\r\njournal = {BIT},<br \/>\r\nvolume = {29},<br \/>\r\npages = {126-139},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {article}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('171','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_171\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1007\/BF01932710\" title=\"Follow DOI:10.1007\/BF01932710\" target=\"_blank\">doi:10.1007\/BF01932710<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('171','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Time-Space Tradeoffs&nbsp;&nbsp;&nbsp;Communication Complexity and Data Streams&nbsp;&nbsp;&nbsp;Verification of Software and Hardware&nbsp;&nbsp;&nbsp;Proof Complexity and Satisfiability&nbsp;&nbsp;&nbsp;Parallel and Distributed Computing&nbsp;&nbsp;&nbsp;Data Structures&nbsp;&nbsp;&nbsp;Circuit and PRAM Lower Bounds&nbsp;&nbsp;&nbsp;Other topics Time-Space Tradeoffs Communication Complexity and Data Streams Verification of Software and Hardware Proof Complexity and Satisfiability Parallel and Distributed Computing Data Structures Circuit and PRAM Lower Bounds Other Topics<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-88","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/pages\/88","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/comments?post=88"}],"version-history":[{"count":19,"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/pages\/88\/revisions"}],"predecessor-version":[{"id":183,"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/pages\/88\/revisions\/183"}],"wp:attachment":[{"href":"https:\/\/homes.cs.washington.edu\/~beame\/site\/wp-json\/wp\/v2\/media?parent=88"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}