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A Compressed Breadth-First Search for Satisfiability

  • DoRon B. Motter
  • Igor L. Markov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2409)

Abstract

Leading algorithms for Boolean satisfiability (SAT) are based on either a depth-first tree traversal of the search space (the DLL procedure [6]) or resolution (the DP procedure [7]). In this work we introduce a variant of Breadth-First Search (BFS) based on the ability of Zero-Suppressed Binary Decision Diagrams (ZDDs) to compactly represent sparse or structured collections of subsets. While a BFS may require an exponential amount of memory, our new algorithm performs BFS directly with an implicit representation and achieves unconventional reductions in the search space.

We empirically evaluate our implementation on classical SAT instances difficult for DLL/DP solvers. Our main result is the empirical Θ(n 4) runtime for hole-n instances, on which DLL solvers require exponential time.

Keywords

Directed Acyclic Graph Implicit Representation Conjunctive Normal Form Truth Assignment Binary Decision Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    F. A. Aloul, I. L. Markov, and K. A. Sakallah. Faster SAT and Smaller BDDs via Common Function Structure. Proc. Intl. Conf. Computer-Aided Design, 2001.Google Scholar
  2. 2.
    F. A. Aloul, M. Mneimneh, and K. A. Sakallah. Backtrack Search Using ZBDDs. Intl. Workshop on Logic and Synthesis, (IWLS), 2001.Google Scholar
  3. 3.
    P. Beame and R. Karp. The efficiency of resolution and Davis-Putnam procedures. submitted for publication.Google Scholar
  4. 4.
    P. Chatalic and L. Simon. Multi-Resolution on Compressed Sets of Clauses. Proc. of 12th International Conference on Tools with Artificial Intelligence (ICTAI-2000), November 2000.Google Scholar
  5. 5.
    P. Chatalic and L. Simon. ZRes: the old DP meets ZBDDs. Proc. of the 17th Conf. of Autom. Deduction (CADE), 2000.Google Scholar
  6. 6.
    M. Davis, G. Logemann, and D. Loveland. A Machine Program for Theorem Proving. Comm. ACM, 5:394–397, 1962.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    M. Davis and H. Putnam. A computing procedure for quantification theory. Jounal of the ACM, 7:201–215, 1960.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    P. Ferragina and G. Manzini. An experimental study of a compressed index. Proc. 12th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2001.Google Scholar
  9. 9.
    R. Gasser. Harnessing Computational Resources for Efficient Exhaustive Search. PhD thesis, Swiss Fed Inst Tech, Zurich, 1994.Google Scholar
  10. 10.
    R. L. Graham, M. Grötschel, and L. Lovász, editors. Handbook of Combinatorics. MIT Press, January 1996.Google Scholar
  11. 11.
    J. F. Groote and H. Zantema. Resolution and binary decision diagrams cannot simulate each other polynomially. Technical Report UU-CS-2000-14, Utrecht University, 2000.Google Scholar
  12. 12.
    A. San Miguel. Random 3-SAT and BDDs: The Plot Thickens Further. CP, 2001.Google Scholar
  13. 13.
    S. Minato. Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems. 30th ACM/IEEE DAC, 1993.Google Scholar
  14. 14.
    A. Mishchenko. An Introduction to Zero-Suppressed Binary Decision Diagrams. http://www.ee.pdx.edu/~alanmi/research/.
  15. 15.
    A. Mishchenko. EXTRA v. 1.3: Software Library Extending CUDD Package: Release 2.3.x. http://www.ee.pdx.edu/~alanmi/research/extra.htm.
  16. 16.
    M. Moskewicz et al. Chaff: Engineering an Efficient SAT Solver. Proc. of IEEE/ACM DAC, pages 530–535, 2001.Google Scholar
  17. 17.
    J. P. Marques Silva and K. A. Sakallah. GRASP: A new search algorithm for satisfiability. ICCAD, 1996.Google Scholar
  18. 18.
    F Somenzi. CUDD: CU Decision Diagram Package Release 2.3.1. http://vlsi.colorado.edu/~fabio/CUDD/cuddIntro.html.
  19. 19.
    T. E. Uribe and M. E. Stickel. Ordered binary decision diagrams and the Davis-Putnam procedure. In J. P. Jouannaud, editor, 1st Intl. Conf. on Constraints in Comp. Logics, volume 845 of LNCS, pages 34–49. Springer, September 1994.CrossRefGoogle Scholar
  20. 20.
    Urquhart. Hard examples for resolution. Journal of the ACM, 34, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • DoRon B. Motter
    • 1
  • Igor L. Markov
    • 1
  1. 1.Department of EECSUniversity of MichiganAnn Arbor

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