KI - Künstliche Intelligenz

, Volume 24, Issue 1, pp 15–23 | Cite as

A SAT Solver for Circuits Based on the Tableau Method

Fachbeitrag
  • 122 Downloads

Abstract

We present an extension of the BC tableau, a calculus for determining satisfiability of constrained Boolean circuits. We argue that a satisfiability decision procedure based on the BC tableau can be implemented as a non-clausal DPLL procedure and that therefore, advances to the DPLL framework can be integrated into such a tableau procedure. We present a prototypical implementation of these ideas and evaluate it using a set of benchmark instances. We show that the extensions increase the efficiency of the basic BC tableau considerably and compare the performance of our solver with that of the non-clausal solver NoClause and the CNF-based SAT solver MiniSat.

References

  1. 1.
    Baaz M, Egly U, Leitsch A (2001) Normal form Transformations. In: Robinson JA, Voronkov A (eds) Handbook of automated reasoning, vol 1. Elsevier Science, Amsterdam, pp 273–333 CrossRefGoogle Scholar
  2. 2.
    Bayardo RJ Jr., Schrag RC (1997) Using CSP look-back techniques to solve real-world SAT instances. In: Proceedings AAAI. AAAI/MIT, Menlo Park, pp 203–208 Google Scholar
  3. 3.
    Biere A, Cimatti A, Clarke EM, Fujita M, Zhu Y (1999) Symbolic model checking using SAT procedures instead of BDDs. In: Proceedings DAC, pp 317–320 Google Scholar
  4. 4.
    Boy de la Tour T (1992) An optimality result for clause form translation. J Symb Comput 14(4):283–301 MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cook SA (1971) The complexity of theorem-proving procedures. In: Proceedings STOC, pp 151–158 Google Scholar
  6. 6.
    Cook SA, Reckhow R (1979) The relative efficiency of propositional proof systems. J Symb Log 44(1):36–50 MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    D’Agostino M (1992) Are tableaux an improvement on truth-tables? Cut-free proofs and bivalence. J Log Lang Inf 1:235–252 MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    D’Agostino M, Mondadori M (1994) The taming of the cut. Classical refutations with analytic cut. J Log Comput 4(3):285–319 MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Davis M, Logemann G, Loveland D (1962) A machine program for theorem-proving. Commun. ACM 5(7):394–397 MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Davis M, Putnam H (1960) A computing procedure for quantification theory. J. ACM 7(3):201–215 MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Drechsler R, Juntilla TA, Niemelä I, (2009) Non-clausal SAT and ATPG. In: Handbook of satisfiability. IOS Press, Amsterdam Google Scholar
  12. 12.
    Eén N, Sörensson N (2006) MiniSAT v2. 0 (beta). Solver description, SAT race Google Scholar
  13. 13.
    Egly U, Seidl M, Woltran S (2009) A solver for QBFs in negation normal form. Constraints 14(1):38–79 MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ganai MK, Ashar P, Gupta A, Zhang L, Malik S (2002) Combining strengths of circuit-based and CNF-based algorithms for a high-performance SAT solver. In: Proceedings DAC, pp 747–750 Google Scholar
  15. 15.
    Gentzen G (1935) Untersuchungen über das logische Schließen. Math Z 39:176–210, 405–431 CrossRefMathSciNetGoogle Scholar
  16. 16.
    Haller L (2008) Extending a tableau-based SAT procedure with techniques from CNF-based SAT. Master’s thesis, Vienna University of Technology, Austria, December 2008 Google Scholar
  17. 17.
    Jain H, Bartzis C, Clarke EM (2006) Satisfiability checking of non-clausal formulas using general matings. In: Proceedings SAT. LNCS, vol 4121. Springer, Berlin, pp 75–89 Google Scholar
  18. 18.
    Järvisalo M, Junttila T (2009) Limitations of restricted branching in clause learning. Constraints 14(3):325–356 MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Järvisalo M, Niemelä I (2008) The effect of structural branching on the efficiency of clause learning SAT solving: an experimental study. J Algorithms 63(1–3):90–113 MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Junttila TA, Niemelä I (2000) Towards an efficient tableau method for Boolean circuit satisfiability checking. In: Proceedings CL. LNCS, vol 1861. Springer, Berlin, pp 553–567 Google Scholar
  21. 21.
    Kröning D, Strichman O (2008) Decision procedures for propositional logic. In: Decision procedures. Springer, Berlin, pp 25–57 CrossRefGoogle Scholar
  22. 22.
    Kuehlmann A, Ganai MK, Paruthi V (2001) Circuit-based Boolean reasoning. In: Proceedings DAC, pp 232–237 Google Scholar
  23. 23.
    Marques-Silva JP, Sakallah KA (1999) Grasp: a search algorithm for propositional satisfiability. IEEE Trans Comput 48(5):506–521 CrossRefMathSciNetGoogle Scholar
  24. 24.
    Moskewicz MW, Madigan CF, Zhao Y, Zhang L, Malik S (2001) Chaff: engineering an efficient SAT solver. In: Proceedings DAC, pp 530–535 Google Scholar
  25. 25.
    Pipatsrisawat K, Darwiche A (2007) A lightweight component caching scheme for satisfiability solvers. In: Proceedings SAT. LNCS, vol 4501. Springer, Berlin, pp 294–299 Google Scholar
  26. 26.
    Plaisted DA, Greenbaum S (1986) A structure-preserving clause form translation. J Symb Comput 2(3):293–304 MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Thiffault C, Bacchus F, Walsh T (2004) Solving non-clausal formulas with DPLL search. In: Proceedings CP. LNCS, vol 3258. Springer, Berlin, pp 663–678 Google Scholar
  28. 28.
    Tseitin GS (1968) On the complexity of derivation in propositional calculus. Stud Constr Math Math Log 2:115–125 Google Scholar
  29. 29.
    Wu CA, Lin TH, Lee CC, Huang CYR (2007) QuteSAT: a robust circuit-based SAT solver for complex circuit structure. In: Proceedings DATE, pp 1313–1318 Google Scholar
  30. 30.
    Zhang L, Madigan CF, Moskewicz MH, Malik S (2001) Efficient conflict driven learning in a Boolean satisfiability solver. In: Proceedings ICCAD. IEEE, New York, pp 279–285 Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute of Information Systems 184/3, KBS GroupTU WienWienÖsterreich
  2. 2.Oxford University Computing LaboratoryOxfordUK

Personalised recommendations