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A Stochastic Non-CNF SAT Solver

  • Rafiq Muhammad
  • Peter J. Stuckey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4099)

Abstract

Stochastic local search techniques have been successful in solving propositional satisfiability (SAT) problems encoded in conjunctive normal form (CNF). Recently complete solvers have shown that there are advantages to tackling propositional satisfiability problems in a more expressive natural representation, since the conversion to CNF can lose problem structure and introduce significantly more variables to encode the problem. In this work we develop a non-CNF SAT solver based on stochastic local search techniques. Crucially the system must be able to represent how true a proposition is and how false it is, as opposed to the usual stochastic methods which represent simply truth or degree of falsity (penalty). Our preliminary experiments show that on certain benchmarks the non-CNF local search solver can outperform highly optimized CNF local search solvers as well as existing CNF and non-CNF complete solvers.

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References

  1. 1.
    Armando, A., Giunchiglia, E.: Embedding complex decision procedures inside an interactive theorem prover. Ann. Math. Artif. Intell. 8(3-4), 475–502 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Crawford, J., Auton, L.: Experimental results on the crossover point in random 3-SAT. Artif. Intell. 81(1-2), 31–57 (1996)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Zhang, H., Stickel, M.: Implementing the Davis-Putnam method. J. Autom. Reasoning 24(1/2), 277–296 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Giunchiglia, E., Sebastiani, R.: Applying the Davis-Putnam procedure to non-clausal formulas. In: AI*IA, pp. 84–94 (1999)Google Scholar
  6. 6.
    Thiffault, C., Bacchus, F., Walsh, T.: Solving non-clausal formulas with DPLL search. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 663–678. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability problems. In: AAAI, pp. 440–446 (1992)Google Scholar
  8. 8.
    McAllester, D.A., Selman, B., Kautz, H.A.: Evidence for invariants in local search. In: AAAI/IAAI, pp. 321–326 (1997)Google Scholar
  9. 9.
    Sebastiani, R.: Applying GSAT to non-clausal formulas (research note). J. Artif. Intell. Res (JAIR) 1, 309–314 (1994)zbMATHGoogle Scholar
  10. 10.
    Kautz, H., Selman, B., McAllester, D.: Exploiting variable dependency in local search. In: Abstracts of the Poster Session of IJCAI 1997 (1997)Google Scholar
  11. 11.
    Stachniak, Z.: Going non-clausal. In: 5th International Symposium on Theory and Applications of Satisfiability Testing (2002)Google Scholar
  12. 12.
    Selman, B., Kautz, H., Cohen, B.: Noise strategies for improving local search. In: AAAI, pp. 337–343 (1994)Google Scholar
  13. 13.
    Bacchus, F., Walsh, T.: A non-CNF DIMACS style (2005), Available from http://www.ssatcompetition.org/2005/
  14. 14.
    Van Hentenryck, P., Michel, L.: Localizer. Constraints 5, 41–82 (2000)Google Scholar
  15. 15.
    Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Navarro, J.A., Voronkov, A.: Generation of hard non-clausal random satisfiability problems. In: AAAI, pp. 436–442 (2005)Google Scholar
  17. 17.
    Crawford, J., Kearns, M., Schapire, R.: The minimal disagreement parity problem as a hard satisfiability problem (unpublished manuscript, 1995)Google Scholar
  18. 18.
    Hoos, H.H., Stützle, T.: Systematic vs. local search for sat. In: Burgard, W., Christaller, T., Cremers, A.B. (eds.) KI 1999. LNCS (LNAI), vol. 1701, pp. 289–293. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  19. 19.
    Wah, B.W., Shang, Y.: A discrete lagrangian-based global-search method for solving satisfiability problems. J. of Global Optimization 12 (1998)Google Scholar
  20. 20.
    Van Hentenryck, P., Michel, L.: Constraint-Based Local Search. MIT Press, Cambridge (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rafiq Muhammad
    • 1
  • Peter J. Stuckey
    • 1
  1. 1.NICTA Victoria Laboratory, Department of Computer Science and Software EngineeringThe University of MelbourneAustralia

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