# First Project: Satisfiability Solvers

## Due Date: Wednesday, November 10, 1999

In this project you will implement a systematic satisfiability solver and a stochastic one, study them experimentally, and design and test your own improved solver.

## What to do:

• Implement:
• The DPLL systematic satisfiability solver.
• The WALKSAT stochastic satisfiability solver.
• A generator of satisfiability problems in CNF (conjunctive normal form).

• This generator will input the desired number of variables, clauses, variables per clause, and any other parameters you may decide to allow, and output a random CNF formula. Successive calls to the generator should produce different random CNFs.
• Study and compare the two solvers empirically.

• Characterize the hard and easy (types of) problems for each. Identify the similarities and differences between the problems that are hard for DPLL and those that are hard for WALKSAT. "Hard" and "easy" should be measured in terms of how long it takes to produce an answer, be it positive or negative (and of the percentage of problems for which the time bounds you set were exceeded).  In other words, the fundamental dependent variable in your empirical study will be the time to solution, and the independent variables will be the parameters you allow in the generator and relations among them (e.g., the ratio of clauses to variables). Note that the algorithms may require significant parameter tuning to perform well, and that this tuning is a significant part of the empirical work. Your writeup (see below) should discuss this process and what you learned from it.

## What to turn in:

• The code you wrote: DPLL, WALKSAT, your own algorithm, problem generator(s), and any other code you used to run experiments. The code should be clear and reasonably documented (comments, brief description of architecture / guide to the code, and brief  user manual).  Also include instructions for building the executables and any command line options the grading program should use.
• A description of what parts of the project were done by each of the two group members.
• An article describing your proposals, experiments and results. This article should be written as a research article for submission to a conference. It should have a maximum of 20 letter-sized pages in 12pt font with 1" margins, including all tables and figures, but excluding references. The project will be graded according to the AAAI review form. Research articles typically have sections describing: the problem they address and its motivation; the new solution(s) proposed, and the rationale for them; empirical and/or theoretical evidence for their superiority to previous approaches; a discussion of relations between the new proposals and previous research, including a candid description of the new approach's limitations and disadvantages; and directions for future research. Citations made in the body of the paper are collected in a list of references at the end. If the algorithm(s) you proposed didn't outperform DPLL and WALKSAT, you can propose (and possibly test) your explanation(s) in the empirical and/or discussion sections.
We may ask you to do a demo / oral discussion of the project.
Acceptable languages for the project are: LISP, C/C++, and Java. Other languages may be allowed by special request.

Much of the recent research on satisfiability has appeared in AAAI, the National Conference on Artificial Intelligence. The proceedings are available in the library, and many of the papers can be found online.

## Standard file formats to be used:

Your sat-solver should accept files of the following format:
```numvars
numclauses
clauselength
clause1
clause2
...
clausen```
Where numvars, numclauses and clauselength are integers and the format for a clause is a parenthesized list of literals.
`( lit1 lit2 ... litm )`
Literals will be represented by integers, with negated literals represented by negative numbers. For example, the 5-clause, 4-variable 3-CNF formula
```( A1 v ~A2 v A3) ^ ( ~A3 v ~A1 v A4 ) ^ ( A2 v A1 v ~A4 )
^ ( ~A2 v A3 v ~A4) v ( ~A1 v A2 v A3 )```
Would be represented by the file:
```4
5
3
( 1 -2 3 )
( -3 -1 4 )
( 2 1 -4 )
( -2 3 -4 )
( -1 2 3 )```
The program should have, somewhere in its output, a line that reads "Solution:" followed by a line with the string "Fail" if no solution was found or a parenthesized list of variable assignments sorted by variable number.  So for the input above, the program might print:
```Solution:
( 1 2 -3 -4 )```
Meaning that the variable assignment:
A1 = True, A2 = True, A3 = False, A4 = False
was found as a solution to this problem.

Note the spaces before and after each literal in the above i/o formats. The grading program will require that you follow the correct format exactly.

Your program should be able to read the test file from the standard input stream. Any parameters your program uses should be set using command line options.  For example, if you want to be able to control the number of restarts and flips, you should create command line options.

`walksat -r10000 -f1000 < problem.wff > problem.out`
The generate program should take at least three inputs: numvars, numclauses and clauselen. Any other inputs you'd like to specify should be clearly documented.

## Code provided:

To help with the experimentation phase, we are providing some infrastructure. The file run-exp.pl will do multiple runs of your program over test files.  See the file itself for a description of how to use it.  The file check-soln.pl will check that the solution returned by your solver is valid.  They're both perl scripts, so after saving them on a unix system, you'll have to make them executable.
`chmod 700 run-exp.pl check-soln.pl`
Good luck!