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A Branching Heuristics for Quantified Renamable Horn Formulas

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Book cover Theory and Applications of Satisfiability Testing (SAT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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References

  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. 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. 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)

    Chapter  Google Scholar 

  4. Rintanen, J.: Constructing Conditional Plans by a Theorem-Prover. Journal of Artificial Intelligence Research 10, 323–352 (1999)

    MATH  Google Scholar 

  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. 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. Rintanen, J.: Improvements to the Evaluation of Quantified Boolean Formulae. In: IJCAI 1999, Stockholm (Sweden), pp. 1192–1197 (1999)

    Google Scholar 

  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. 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. Giunchiglia, E., Narizzano, M., Tacchella, A.: Backjumping for Quantified Boolean Logic Satisfiability. In: IJCAI 2001, Seattle (USA), pp. 275–281 (2001)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Article  MATH  MathSciNet  Google Scholar 

  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. Kleine-Büning, H., Karpinski, M., Flögel, A.: Resolution for quantified boolean formulas. Information and Computation 117, 12–18 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hébrard, J.J.: A Linear Algorithm for Renaming a Set of Clauses as a Horn Set. Theoretical Computer Science 124, 343–350 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Jeroslow, R.J., Wang, J.: Solving propositional satisfiability problems. Annals of Mathematics and Artificial Intelligence 1, 167–188 (1990)

    Article  MATH  Google Scholar 

  20. Freemann, J.W.: Improvement to Propositional Satisfiability Search Algorithms. PhD thesis, University of Pennsylvania (1995)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  22. Balsiger, P., Heuerding, A., Schwendimann, S.: A benchmark method for the propositional modal logics K, KT, S4. Automated Reasoning 24, 297–317 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. CRIL, CNRS FRE 2499,  

    Sylvie Coste-Marquis, Daniel Le Berre & Florian Letombe

Authors
  1. Sylvie Coste-Marquis
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  2. Daniel Le Berre
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  3. Florian Letombe
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Toronto, Canada

    Fahiem Bacchus

  2. Dept. of Computer Science, Trinity College, Dublin 2

    Toby Walsh

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Coste-Marquis, S., Le Berre, D., Letombe, F. (2005). A Branching Heuristics for Quantified Renamable Horn Formulas. In: Bacchus, F., Walsh, T. (eds) Theory and Applications of Satisfiability Testing. SAT 2005. Lecture Notes in Computer Science, vol 3569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499107_30

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  • DOI: https://doi.org/10.1007/11499107_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26276-3

  • Online ISBN: 978-3-540-31679-4

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