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Variable and Clause Ordering in an FSA Approach to Propositional Satisfiability

  • José M. Castaño
  • Rodrigo Castaño
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6807)

Abstract

We use a finite state (FSA) construction approach to address the problem of propositional satisfiability (SAT). We use a very simple translation from formulas in conjunctive normal form (CNF) to regular expressions and use regular expressions to construct an FSA. As a consequence of the FSA construction, we obtain an ALL-SAT solver and model counter. We compare how several variable ordering (state ordering) heuristics affect the running time of the FSA construction. We also present a strategy for clause ordering (automata composition). We compare the running time of state-of-the-art model counters, BDD based sat solvers and we show that this FSA approach obtains state-of-the-art performance on some hard unsatisfiable benchmarks. This work brings up many questions on the possible use of automata to address SAT.

Keywords

ALL-SAT model counting FSA intersection regular expression compilation 

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References

  1. 1.
    Aloul, F., Lynce, I., Prestwich, S.: Symmetry Breaking in Local Search for Unsatisfiability. In: 7th International Workshop on Symmetry and Constraint Satisfaction Problems, Providence, RI (2007)Google Scholar
  2. 2.
    Aloul, F.A., Markov, I.L., Sakallah, K.A.: FORCE: a fast and easy-to-implement variable-ordering heuristic. In: ACM Great Lakes Symposium on VLSI, pp. 116–119. ACM Press, New York (2003)Google Scholar
  3. 3.
    Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult SAT instances in the presence of symmetry. In: DAC, pp. 731–736. ACM Press, New York (2002)Google Scholar
  4. 4.
    Barton, G.E.: Computational complexity in two-level morphology. In: Proc. of the 24th ACL, New York, pp. 53–59 (1986)Google Scholar
  5. 5.
    Beesley, K., Karttunen, L.: Finite State Morphology. CSLI Publications (2003)Google Scholar
  6. 6.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2009)zbMATHGoogle Scholar
  7. 7.
    Büchi, J.R.: Weak second-order arithmetic and finite automata. Zeit. Math. Logik. Grund. Math. 66–92 (1960)Google Scholar
  8. 8.
    Castaño, J.: Two views on crossing dependencies, language, biology and satisfiability. In: 1st International Work-Conference on Linguistics, Biology and Computer Science: Interplays. IOS Press, Amsterdam (2011)Google Scholar
  9. 9.
    Darwiche, A.: New Advances in Compiling CNF into Decomposable Negation Normal Form. In: ECAI, pp. 328–332 (2004)Google Scholar
  10. 10.
    Elgot, C.C.: Decision problems of automata design and related arithmetics. Transactions of the American Mathematical Society (1961)Google Scholar
  11. 11.
    Franco, J., Kouril, M., Schlipf, J., Ward, J., Weaver, S., Dransfield, M.R., Vanfleet, W.M.: SBSAT: a state-based, BDD-based satisfiability solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 398–410. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Gomes, C.P., Sabharwal, A., Selman, B.: Model Counting. In: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 633–654. IOS Press, Amsterdam (2009)Google Scholar
  13. 13.
    Hadzic, T., Hansen, E.R., O’Sullivan, B.: On Automata. In: MDDs and BDDs in Constraint Satisfaction (2008)Google Scholar
  14. 14.
    Hansen, P., Jaumard, B.: Algorithms for the maximum satisfiability problem. Computing 44, 279–303 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lange, K., Rossmanith, P.: The emptiness problem for intersections of regular languages. In: Havel, I.M., Koubek, V. (eds.) MFCS 1992. LNCS, vol. 629, pp. 346–354. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  16. 16.
    Lewis, H.R., Papadimitriou, C.H.: Elements of the Theory of Computation, 2nd edn. Prentice-Hall, Upper Saddle River (1997)Google Scholar
  17. 17.
    Marek, V.W.: Introduction to Mathematics of Satisfiability. Chapman and Hall/CRC (2010)Google Scholar
  18. 18.
    Muise, C., Beck, J.C., McIlraith, S.: Fast d-DNNF Compilation with sharpSAT (2010)Google Scholar
  19. 19.
    Sinz, C., Biere, A.: Extended resolution proofs for conjoining bDDs. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 600–611. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Tapanainen, P.: Applying a Finite-State Intersection Grammar. In: Roche, E., Schabes, Y. (eds.) Finite-State Language Processing, pp. 311–327. MIT Press, Cambridge (1997)Google Scholar
  21. 21.
    Thurley, M.: sharpSAT – counting models with advanced component caching and implicit BCP. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 424–429. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Urquhart, A.: Hard examples for resolution. J. ACM 34(1), 209–219 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Vardi, M.: Logic and Automata: A Match Made in Heaven. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 193–193. Springer, Heidelberg (2003)Google Scholar
  24. 24.
    Vardi, M.Y., Wolper, P.: Automata-Theoretic techniques for modal logics of programs. J. Comput. Syst. Sci. 32, 183–221 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Vempaty, N.R.: Solving Constraint Satisfaction Problems Using Finite State Automata. In: AAAI, pp. 453–458 (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • José M. Castaño
    • 1
  • Rodrigo Castaño
    • 1
  1. 1.Depto. de ComputaciónFCEyN, UBAArgentina

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