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Effective Preprocessing with Hyper-Resolution and Equality Reduction

  • Fahiem Bacchus
  • Jonathan Winter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2919)

Abstract

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.

Keywords

Inference Rule Unit Propagation Transitive Closure Graph Search Unit Clause 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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. 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. 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
  4. 4.
    Simon, L., Berre, D.L., Hirsch, E.A.: The sat2002 competition. Technical report (2002), www.satlive.org, available on line at www.satlive.org/SATCompetition/
  5. 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. 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
  7. 7.
    Aspvall, B., Plass, M., Tarjan, R.: A linear-time algorithms for testing the truth of certain quantified boolean formulas. Information Processing Letters 8, 121–123 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 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. 9.
    Morrisette, T.: Incremental reasoning in less time and space (2002) (submitted manuscript), available from the author e-mail threesat2000@yahoo.com Google Scholar
  10. 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
  11. 11.
    Tarjan, R.: Depth first search and linear graph algorithms. SIAM Journal on Computing 1, 146–160 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Crawford, J.M., Auton, L.D.: Experimental results on the crossover point in random 3-sat. Artificial Intelligence 81, 31–57 (1996)CrossRefMathSciNetGoogle Scholar
  13. 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. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Fahiem Bacchus
    • 1
  • Jonathan Winter
    • 1
  1. 1.Department of Computer ScienceUniversity of Of TorontoTorontoCanada

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