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A Branching Heuristics for Quantified Renamable Horn Formulas

  • Sylvie Coste-Marquis
  • Daniel Le Berre
  • Florian Letombe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)

Abstract

Many solvers have been designed for \(\mathcal{QBF}\)s, the validity problem for Quantified Boolean Formulas for the past few years. In this paper, we describe a new branching heuristics whose purpose is to promote renamable Horn formulas. This heuristics is based on Hébrard’s algorithm for the recognition of such formulas. We present some experimental results obtained by our qbf solver Qbfl with the new branching heuristics and show how its performances are improved.

Keywords

Modal Logic Boolean Formula Validity Problem Information Processing Letter Quantify Boolean Formula 
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.
    Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving advanced reasoning tasks using quantified boolean formulas. In: AAAI 2000, Austin (USA), pp. 417–422 (2000)Google Scholar
  2. 2.
    Fargier, H., Lang, J., Marquis, P.: Propositional Logic and One-stage Decision Making. In: KR 2000, Breckenridge (CO), pp. 445–456 (2000)Google Scholar
  3. 3.
    Besnard, P., Schaub, T., Tompits, H., Woltran, S.: Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 320–331. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Rintanen, J.: Constructing Conditional Plans by a Theorem-Prover. Journal of Artificial Intelligence Research 10, 323–352 (1999)zbMATHGoogle Scholar
  5. 5.
    Pan, G., Sattler, U., Vardi, M.Y.: BDD-Based Decision Procedures for K. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 16–30. Springer, Heidelberg (2002)Google Scholar
  6. 6.
    Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to Evaluate Quantified Boolean Formulae. In: AAAI 1998, Madison (USA), pp. 262–267 (1998)Google Scholar
  7. 7.
    Rintanen, J.: Improvements to the Evaluation of Quantified Boolean Formulae. In: IJCAI 1999, Stockholm (Sweden), pp. 1192–1197 (1999)Google Scholar
  8. 8.
    Feldmann, R., Monien, B., Schamberger, S.: A distributed algorithm to evaluate quantified boolean formula. In: AAAI 2000, Austin (USA), pp. 285–290 (2000)Google Scholar
  9. 9.
    Rintanen, J.: Partial implicit unfolding in the Davis-Putnam procedure for Quantified Boolean Formulae. In: QBF 2001, Siena (Italy), pp. 84–93 (2001)Google Scholar
  10. 10.
    Giunchiglia, E., Narizzano, M., Tacchella, A.: Backjumping for Quantified Boolean Logic Satisfiability. In: IJCAI 2001, Seattle (USA), pp. 275–281 (2001)Google Scholar
  11. 11.
    Letz, R.: Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, p. 160. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Zhang, L., Malik, S.: Towards a symetric treatment of satisfaction and conflicts in quantified boolean formula evaluation. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 200–215. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Pan, G., Vardi, M.: Optimizing a BDD-Based Modal Solver. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 75–89. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Audemard, G., Saïs, L.: SAT based BDD solver for Quantified Boolean Formulas. In: ICTAI 2004, Boca Raton (USA), pp. 82–89 (2004)Google Scholar
  15. 15.
    Aspvall, B., Plass, M., Tarjan, R.: A linear-time algorithm for testing the truth of certain quantified boolean formulas. Information Processing Letters 8, 121–123 (1979); Erratum: Information Processing Letters 14(4), 195 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Gent, I.P., Rowley, A.: Solving 2-CNF Quantified Boolean Formulae using Variable Assignment and Propagation. In: QBF 2002, Cincinnati (USA), pp. 17–25 (2002)Google Scholar
  17. 17.
    Kleine-Büning, H., Karpinski, M., Flögel, A.: Resolution for quantified boolean formulas. Information and Computation 117, 12–18 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Hébrard, J.J.: A Linear Algorithm for Renaming a Set of Clauses as a Horn Set. Theoretical Computer Science 124, 343–350 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Jeroslow, R.J., Wang, J.: Solving propositional satisfiability problems. Annals of Mathematics and Artificial Intelligence 1, 167–188 (1990)zbMATHCrossRefGoogle Scholar
  20. 20.
    Freemann, J.W.: Improvement to Propositional Satisfiability Search Algorithms. PhD thesis, University of Pennsylvania (1995)Google Scholar
  21. 21.
    Le Berre, D., Simon, L., Tacchella, A.: Challenges in the QBF Arena: the SAT 2003 evaluation of QBF solvers. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 468–485. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Balsiger, P., Heuerding, A., Schwendimann, S.: A benchmark method for the propositional modal logics K, KT, S4. Automated Reasoning 24, 297–317 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Biere, A.: Resolve and Expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sylvie Coste-Marquis
    • 1
  • Daniel Le Berre
    • 1
  • Florian Letombe
    • 1
  1. 1.CRIL, CNRS FRE 2499 

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