#lang scribble/base
@(require racket)
@(require scribble/core)
@(require scribble/html-properties)

@(define Racket (hyperlink "http://racket-lang.org" "Racket"))
@(define Z3 (hyperlink "http://research.microsoft.com/en-us/um/redmond/projects/z3/" "Z3"))
@(define xpose3 (hyperlink "../xpose/xpose3.sk" "xpose3.sk"))
@(define xpose2 (hyperlink "../xpose/xpose2.sk" "xpose2.sk"))
@(define xpose3-QF_AUFLIA (hyperlink "../xpose/xpose3-QF_AUFLIA.smt2" "QF_AUFLIA encoding"))
@(define L3 (hyperlink "../L3.pdf" "Lecture 3"))
@(define hw-style (make-style "hw-style" (list (make-css-addition "hw-style.css"))))

@title[#:style @hw-style]{CS294 HW 2}

This assignment builds on the material in @L3, which covers 
the translation of straight-line code into formulas.  To learn 
how to translate programs with control flow, loops, pointers, etc., 
please read the following paper by next Thursday, September 6:

@tabular[(list (list @hspace[5] 
                     @para{Daniel Kroening, Edmund Clarke and Karen Yorav.  
                           @(hyperlink "http://www.cs.cmu.edu/~svc/papers/view-publications-cky03.html" 
                                       "Behavioral Consistency of C and Verilog Programs Using Bounded Model Checking"). 
                           DAC 2003.}
                     @hspace[5]))]


HW 2 is due at 12:00 a.m. on @bold{September 10, 2012}.  

@section[#:tag "part 1"]{A QF_AUFBV encoding of SIMD transpose}

Encode @xpose3 in @Z3, using @emph{only} the theories of arrays and bitvectors.  
There should be no values of sort Int in your encoding.  
You can create the encoding manually, but we suggest writing a script 
to generate it.  Here is the Racket @(hyperlink "../xpose/xpose3-QF_AUFLIA.rkt" "script") 
we showed in @L3 for generating the @(identity @xpose3-QF_AUFLIA).

The encoding should produce values for the holes in @xpose3
so that it correctly transposes the following input matrix:

@verbatim|{ 0  1  2  3
            4  5  6  7
            8  9 10 11
           12 13 14 15}|

@Z3 should be able to solve your QF_AUFBV encoding at least @bold{2 times faster} than the 
@(identity @xpose3-QF_AUFLIA).  On our machines, a bitvector encoding is 
about 6 times faster.  

For this part of the assignment, please @seclink["submit"]{submit} the following:

@itemlist[@item{An @tt{xpose3-QF_AUFBV.smt2} file that contains your encoding.  We will test it using @(identity @Z3).}
          @item{An @tt{xpose3-QF_AUFBV.*} script that contains your generator, if you used one.  If the generator is written 
                  in a language other than Racket or Python, you should also provide complete instructions for 
                  compiling and executing it.}]

         
@section[#:tag "part 2"]{An SMT encoding of SIMD transpose with additional holes}

Encode @xpose2 in @Z3, using any combination of theories you want.  The encoding should work on 
the following input matrix:  

@verbatim|{ 1  2  3  4
            5  6  7  8
            9 10 11 12 
           13 14 15 16}|

We'll hold a contest for the fastest encoding. 

For this part of the assignment, please @seclink["submit"]{submit} the following:

@itemlist[@item{An @tt{xpose2.smt2} file that contains your encoding.  We will test it using @(identity @Z3).}
          @item{An @tt{xpose2.*} script that contains your generator, if you used one.  If the generator is written 
                  in a language other than Racket or Python, you should also provide complete instructions for 
                  compiling and executing it.}]

@section{Extra credit}

Some fun things to try for extra credit:

@itemlist[@item{Win the encoding contest from @seclink["part 2"]{Part 2}!}
          @item{Explain why the input matrix from @seclink["part 1"]{Part 1} does not sufficiently constrain
                the set of programs in @seclink["part 2"]{Part 2}.  That is, the program synthesized in 
                @seclink["part 2"]{Part 2} using the matrix from @seclink["part 1"]{Part 1} will not work on 
                some inputs.  Why?}
          @item{Scale your encoding to larger matrices:  8x8, 16x16, etc.}
          @item{Try using a different solver.}
          @item{Produce an encoding that does not correspond to the operational semantics of transpose.}
          ]

@section[#:tag "submit"]{Submission instructions}

Create a @tt{@emph{username}.zip} archive of all the files specified in  
@seclink["part 1"]{Part 1} and @seclink["part 2"]{Part 2} of the assignment, 
where @emph{username} is your Google Groups ID.  Email the archive to 
@(author+email "" "emina@eecs.berkeley.edu" #:obfuscate? #t) and 
@(author+email "" "bodik@cs.berkeley.edu" #:obfuscate? #t) by 12:00 a.m. on @bold{September 10, 2012}.