Skip to main content
Springer Nature Link
Log in

A Hybrid Approach for SAT

  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming - CP 2002 (CP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2470))

  • 1058 Accesses

Abstract

Exploiting variable dependencies has been shown very useful in local search algorithms for SAT. In this paper, we extend the use of such dependencies by hybridizing a local search algorithm, Walksat, and the DPLL procedure, Satz. At each node reached in the DPLL search tree to a fixed depth, we construct the literal implication graph. Its strongly connected components are viewed as equivalency classes. Each one is substituted by a unique representative literal to reduce the constructed graph and the input formula. Finally, the implication dependencies are closed under transitivity. The resulted implications and equivalencies are exploited by Walksat at each node of the DPLL tree. Our approach is motivated by the power of the branching rule used in Satz that may provide a valid path to a solution, and generate more implications at deep nodes. Experimental results confirm the efficiency of our approach.

This work is partially supported by French CNRS under grant number SUB/2001/0111/DR16

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Y. Asahiro, K. Iwama, and E. Miyano. Random Generation of Test Instances with Controlled Attributes. In D. S. Johnson and M. A. Trick, editors, Cliques, Coloring, and Satisfiability; The Second DIMACS Implementation Challenge, volume 26, pages 377–394, 1996.

    Google Scholar 

  2. L. Brisoux Devendeville, L. Saïs, and E. Grégoire. Recherche locale: vers une exploitation des propriétés structurelles. In proceedings of JNPC’2000, pages 243–244, Marseille, France, 2000.

    Google Scholar 

  3. S. Cook. The Complexity of Theorem Proving Procedures. In Proceeding oh the Third Annual ACM Symp. on Theory of Computing, pages 151–158, 1971.

    Google Scholar 

  4. J. M. Crawford and L. D. Auton. Experimental Results on the Crosover Point in Random 3-SAT. Artificial Intelligence Journal, 81(1–2):31–57, 1996.

    Article  MathSciNet  Google Scholar 

  5. M. Davis, G. Logemann, and D. Loveland. A Machine Program for Theorem Proving. In Communication of ACM Journal, volume 5(7), pages 394–397, July 1962.

    Google Scholar 

  6. F. J. Ferguson and T. Larrabee. Test Pattern Generation for Realistic Bridging Faults in CMOS ICS. In Proceedings of the International Testing Conference, pages 492–499, 1991.

    Google Scholar 

  7. J. W. Freeman. Improvements to Propostional Satisfiability Search Algorithms. PhD thesis, Departement of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, 1995.

    Google Scholar 

  8. J. W. Freeman. Hard Random 3-SAT Problems and the Davis-Putnam Procedure. In Artificial Intelligence Journal, pages 81:183–198, 1996.

    Article  MathSciNet  Google Scholar 

  9. M. L. Ginsberg. Dynamic backtracking. Journal of Artificial Intelligence Research, 1:25–46, 1993.

    MATH  Google Scholar 

  10. M. L. Ginsberg and D. A. McAllester. GSAT and Dynamic Backtracking. In P. Torasso, J. Doyle, and E. Sandewall, editors, Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning KR’94, pages 226–237. Morgan Kaufmann, 1994.

    Google Scholar 

  11. F. Glover and M. Laguna. Tabu Search. Kluwer Academic Publishers, 1997.

    Google Scholar 

  12. J. Gu. Efficient Local Search for Very Large-Scale Satisfiability problems. In ACM SIGART Bulletin, pages 3(1):8–12, 1992.

    Article  Google Scholar 

  13. H. H. Hoos and T. Stutzle. Local search algorithms for SAT: An empirical evaluation. Journal of Automated Reasoning, 24(4):421–481, 2000.

    Article  MATH  Google Scholar 

  14. N. Jussien and O. Lhomme. Local search with constraint propagation and conflict-based heuristics. In Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI’2000), pages 169–174, Austin, TX, USA, August 2000.

    Google Scholar 

  15. H. Kautz, D. McAllester, and B. Selman. Encoding Plans in Propositional Logic. In Proceedings of the 4th International Conference on the Principle of Knowledge Representation and Reasoning, KR’96, pages 374–384, 1996.

    Google Scholar 

  16. H. Kautz and B. Selman. Pushing the Envelope: Planning, Propositional Logic, and Stochastic Search. In Howard Shrobe and Ted Senator, editors, Proceedings of the 13th National Conference on Artificial Intelligence and the 8th Innovative Applications of Artificial Intelligence Conference, pages 1194–1201, Menlo Park, California, 1996.

    Google Scholar 

  17. J. Lang and P. Marquis. Complexity Results for Independence and Definability in Propositional Logic. In A. G. Cohn, L. K. Schubert, and S. C. Shapiro, editors, Proceedings of the Sixth International Conference on Principles of Knowledge Representataion and Reasoning, KR’98, pages 356–367, 1998.

    Google Scholar 

  18. T. Larrabee. Test Pattern Generation Using Boolean Satisfiability. In IEEE Transactions on Computer-Aided Design, pages 11(1):6–22, 1992.

    Article  Google Scholar 

  19. C. M. Li. Exploiting Yet More the Power of Unit Clause Propagation to solve 3-SAT Problem. In ECAI’96 Workshop on Advances in Propositional Deduction, pages 11–16, Budapest, Hungray, 1996.

    Google Scholar 

  20. C. M. Li and Anbulagan. Heuristic Based on Unit Propagation for Satisfiability. In Proceedings of CP’97, Springer-Verlag, LNCS 1330, pages 342–356, Austria, 1997.

    Google Scholar 

  21. B. Mazure, L. Saïs, and E. Grégoire. Boosting Complete Techniques Thanks to Local Search. Annals of Mathematics and Artificial Intelligence, 22(3–4):319–331, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  22. D. McAllester, B. Selman, and H. Kautz. Evidence for Invariants in Local Search. In Proceedings of the 14th National Conference on Artificial Intelligence, AAAI’97, pages 321–326, Providence, Rhode Island, 1997. MIT Press.

    Google Scholar 

  23. B. Selman, H. Kautz, and B. Cohen. Noise Strategies for Improving Local Search. In MIT press, editor, Proceedings of the 12th National Conference on Artificial Intelligence AAAI’94, volume 1, pages 337–343, 1994.

    Google Scholar 

  24. B. Selman, H. Kautz, and D. McAllester. Ten Challenges in Propositional Reasoning and Search. In Proceedings of IJCAI’97, pages 50–54, Nagoya, Aichi, Japan, August 1997.

    Google Scholar 

  25. B. Selman, H. J. Levesque, and D. Mitchell. A New Method for Solving Hard Satisfiability Problems. In Paul Rosenbloom and Peter Szolovits, editors, Proceedings of the 10th National Conference on Artificial Intelligence, AAAI’92, pages 440–446, Menlo Park, California, 1992.

    Google Scholar 

  26. M. N. Velev and R. E. Bryant. Superscalar processor verification using efficient reductions of the logic of equality with uninterpreted functions to propositional logic. In Correct Hardware Design and Verification Methods, CHARME’99, 1999.

    Google Scholar 

  27. H. Zhang and M. E. Stickel. Implementing the davis-putnam method. Journal of Automated Reasoning, 24(1):277–296, 2000.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre LGI2P, éecole des Mines d’Alès, Site EERIE Parc Scientifique Georges Besse, 30035, Cedex 01, Nîes, France

    Djamal Habet & Michel Vasquez

  2. LaRIA, Université de Picardie Jules Verne, 5, Rue du Moulin Neuf, 80000, Amiens, France

    Chu Min Li & Laure Devendeville

Authors
  1. Djamal Habet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chu Min Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Laure Devendeville
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michel Vasquez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Brown University, Box 1910, Providence, RI, 02912, USA

    Pascal Van Hentenryck

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Habet, D., Li, C.M., Devendeville, L., Vasquez, M. (2002). A Hybrid Approach for SAT. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-46135-3_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44120-5

  • Online ISBN: 978-3-540-46135-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics