Effective Preprocessing with Hyper-Resolution and Equality Reduction
HypBinRes, a particular form of hyper-resolution, was first employed in the SAT solver 2cls+eq. In 2cls+eq, HypBinRes and equality reduction are used at every node of a DPLL search tree, pruning much of the search tree. This allowed 2cls+eq to display the best all-around performance in the 2002 SAT solver competition. In particular, it was the only solver to qualify for the second round of the competition in all three benchmark categories. In this paper we investigate the use of HypBinRes and equality reduction in a preprocessor that can be used to simplify a CNF formula prior to SAT solving. We present empirical evidence demonstrating that such a preprocessor can be extremely effective on large structured problems, making some previously unsolvable problems solvable. The preprocessor is also able to solve a number of non-trivial instances by itself. Since the preprocessor does not have to worry about undoing changes on backtrack, nor about keeping track of reasons for intelligent backtracking, we are able to develop a new algorithm for applying HypBinRes that can be orders of magnitude more efficient than the algorithm employed inside of 2cls+eq. The net result is a technique that improves our ability to solve hard problems SAT problems.
KeywordsInference Rule Unit Propagation Transitive Closure Graph Search Unit Clause
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- 1.Bacchus, F.: Enhancing davis putnam with extended binary clause reasoning. In: Proceedings of the AAAI National Conference, pp. 613–619 (2002)Google Scholar
- 2.Bacchus, F.: Exploring the computational tradeoff of more reasoning and less searching. In: Fifth International Symposium on Theory and Applications of Satisfiability Testing, SAT 2002, pp. 7–16 (2002), Available from www.cs.toronto.edu/~fbacchus/2clseq.html
- 3.Van Gelder, A., Tsuji, Y.K.: Satisfiability testing with more reasoning and less guessing. In: Johnson, D., Trick, M. (eds.) Cliques, Coloring and Satisfiability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 559–586. American Mathematical Society, Providence (1996)Google Scholar
- 5.Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient sat solver. In: Proc. of the Design Automation Conference, DAC (2001)Google Scholar
- 6.Lynce, I., Marques-Silva, J.P.: The puzzling role of simplification in propositional satisfiability. In: EPIA 2001 Workshop on Constraint Satisfaction and Operational Research Techniques for Problem Solving (EPIA-CSOR) (2001), available on line at sat.inesc.pt/~jpms/research/publications.html
- 8.Brafman, R.I.: A simplifier for propositional formulas with many binary clauses. In: Proceedings of the International Joint Conference on Artifical Intelligence (IJCAI), pp. 515–522 (2001)Google Scholar
- 9.Morrisette, T.: Incremental reasoning in less time and space (2002) (submitted manuscript), available from the author e-mail email@example.com Google Scholar
- 10.Van Gelder, A.: Toward leaner binary-clause reasoning in a satisfiability solver. In: Fifth International Symposium on the Theory and Applications of Satisfiability Testing, SAT 2002 (2002), on line pre-prints available at gauss.ececs.uc.edu/Conferences/SAT2002/sat2002list.html
- 13.Li, C.M.: Anbulagan: Heuristics based on unit propagation for satisfiability problems. In: Proceedings of the International Joint Conference on Artifical Intelligence (IJCAI), pp. 366–371 (1997)Google Scholar
- 14.Berre, D.L.: Exploiting the real power of unit propagation lookahead. In: LICS Workshop on Theory and Applications of Satisfiablity Testing (2001)Google Scholar