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AVAL: An Enumerative Method for SAT

  • Gilles Audemard
  • Belaid Benhamou
  • Pierre Siegel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1861)

Abstract

We study an algorithm for the SAT problem which is based on the Davis and Putnam procedure. The main idea is to increase the application of the unit clause rule during the search. When there is no unit clause in the set of clauses, our method tries to produce one occuring in the current subset of binary clauses. A literal deduction algorithm is implemented and applied at each branching node of the search tree. This method AVAL is a combination of the Davis and Putnam principle and of the mono-literal deduction procedure. Its efficiency comes from the average complexity of the literal deduction procedure which is linear in the number of variables. The method is called “AVAL” (avalanch) because of its behaviour on hard random SAT problems. When solving these instances, an avalanche of mono-literals is deduced after the first success of literal production and from that point, the search effort is reduced to unit propagations, thus completing the remaining part of enumeration in polynomial time.

Keywords

Satisfiability deduction enumeration 

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References

  1. 1.
    Y. Boufkhad. Aspects probabilistes et algorithmiques du problème de satisfaisabilité. PhD thesis, Univertsité de Jussieu, 1996.Google Scholar
  2. 2.
    V. Chvátal and B. Reed. Mick Gets Some (the odds are on this side). In 33rd IEEE Symposium on Foundation of Computers Science, 1992.Google Scholar
  3. 3.
    M. Davis and H. Putnam. A computing procedure for quantification theory. JACM, 1960.Google Scholar
  4. 4.
    O. Dubois, P. André, Y. Boufkhad, and J. Carlier. Sat versus unsat. AMS, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 26, 1996.Google Scholar
  5. 5.
    O. Dubois and Y. Boufkhad. A General Upper Bound for the Satisfiability Threshold of random r-sat formulae. Journal of Algorithms, 1996.Google Scholar
  6. 6.
    J.W. Freeman. Improvements to Propositionnai Satisfiability Search Algorithms. PhD thesis, Univ. of Pennsylvania, Philadelphia, 1995.Google Scholar
  7. 7.
    J.W. Freeman. Hard random 3-SAT problems and the Davis-Putnam procedure. Artificial Intelligence, 81(2):183–198, 1996.CrossRefMathSciNetGoogle Scholar
  8. 8.
    E. Friegut. Necessary and sufficient conditions for sharp threholds of graphs properties and the k-sat problem. Technical report, Institute of Mathematics, The Hebrew University of Jerusalem, 1997.Google Scholar
  9. 9.
    A. Goerdt. A threshold for unsatisfiability. In Mathematical Foundations of Computer Science, volume 629, pages 264–274. Springer, 1992.MathSciNetGoogle Scholar
  10. 10.
    Chu Min Li and Anbulagan. Heuristics based on unit propagation for satisfiability problem. In proceedings of IJCAI 97, 1997.Google Scholar
  11. 11.
    Chu Min Li and Anbulagan. Look-Ahead Versus Look-Back for Satisfiability Problems. In proceedings of CP97, pages 341–355, 1997.Google Scholar
  12. 12.
    W.V. Quine. Methods of logics. Henry Holt, New York, 1950.Google Scholar
  13. 13.
    B. Selman, H. Levesque, and D. Mitchell. A New Method for Solving Hard Satisfiability Problems. In Proceedings of the 10th National Conference on Artificial Intelligence AAAI’94, 1994.Google Scholar
  14. 14.
    H. Zhang. SATO: An efficient prepositional prover. In Proceedings of the 14th International Conference on Automated deduction, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Gilles Audemard
    • 1
  • Belaid Benhamou
    • 1
  • Pierre Siegel
    • 1
  1. 1.Laboratoire d’Informatique de MarseilleCentre de Mathématiques et d’InformatiqueMarseille cedex 13France

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