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Integrating Dependency Schemes in Search-Based QBF Solvers

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Theory and Applications of Satisfiability Testing – SAT 2010 (SAT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6175))

Abstract

Many search-based QBF solvers implementing the DPLL algorithm for QBF (QDPLL) process formulae in prenex conjunctive normal form (PCNF). The quantifier prefix of PCNFs often results in strong variable dependencies which can influence solver performance negatively. A common approach to overcome this problem is to reconstruct quantifier structure e.g. by quantifier trees. Dependency schemes are a generalization of quantifier trees in the sense that more general dependency graphs can be obtained. So far, dependency graphs have not been applied in QBF solving. In this work we consider the problem of efficiently integrating dependency graphs in QDPLL. Thereby we generalize related work on integrating quantifier trees. By analyzing the core parts of QDPLL, we report on modifications necessary to profit from general dependency graphs. In comprehensive experiments we show that QDPLL using a particular dependency graph, despite of increased overhead, outperforms classical QDPLL relying on quantifier prefixes of PCNFs.

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References

  1. Ayari, A., Basin, D.A.: QUBOS: Deciding Quantified Boolean Logic Using Propositional Satisfiability Solvers. In: Aagaard, M., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 187–201. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Benedetti, M.: Quantifier Trees for QBFs. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 378–385. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Bhalla, A., Lynce, I., de Sousa, J.T., Marques-Silva, J.: Heuristic-Based Backtracking Relaxation for Propositional Satisfiability. Journal of Automated Reasoning (JAR) 35(1-3), 3–24 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. 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 

  5. Bubeck, U., Büning, H.K.: Bounded Universal Expansion for Preprocessing QBF. In: Marques-Silva, Sakallah (eds.) [25], pp. 244–257.

    Google Scholar 

  6. Kleine Büning, H., Karpinski, M., Flögel, A.: Resolution for Quantified Boolean Formulas. Inf. Comput. 117(1), 12–18 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cadoli, M., Giovanardi, A., Schaerf, M.: An Algorithm to Evaluate Quantified Boolean Formulae. In: AAAI/IAAI, pp. 262–267 (1998)

    Google Scholar 

  8. Egly, U., Seidl, M., Tompits, H., Woltran, S., Zolda, M.: Comparing Different Prenexing Strategies for Quantified Boolean Formulas. In: Giunchiglia, Tacchella (eds.) [17], pp. 214–228

    Google Scholar 

  9. Egly, U., Seidl, M., Woltran, S.: A Solver for QBFs in Nonprenex Form. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) ECAI. FAIA, vol. 141, pp. 477–481. IOS Press, Amsterdam (2006)

    Google Scholar 

  10. Gent, I.P., Giunchiglia, E., Narizzano, M., Rowley, A.G.D., Tacchella, A.: Watched Data Structures for QBF Solvers. In: Giunchiglia, Tacchella (eds.) [17], pp. 25–36 (2003)

    Google Scholar 

  11. Giunchiglia, E., Narizzano, M., Tacchella, A.: Quantified Boolean Formulas Satisfiability Library, QBFLIB (2001), http://www.qbflib.org

  12. Giunchiglia, E., Narizzano, M., Tacchella, A.: QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 364–369. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Giunchiglia, E., Narizzano, M., Tacchella, A.: Learning for Quantified Boolean Logic Satisfiability. In: AAAI/IAAI, pp. 649–654 (2002)

    Google Scholar 

  14. Giunchiglia, E., Narizzano, M., Tacchella, A.: Monotone Literals and Learning in QBF Reasoning. In: Wallace (ed.) [31], pp. 260–273 (2004)

    Google Scholar 

  15. Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas. J. Artif. Intell. Res. (JAIR) 26, 371–416 (2006)

    MathSciNet  MATH  Google Scholar 

  16. Giunchiglia, E., Narizzano, M., Tacchella, A.: Quantifier Structure in Search-Based Procedures for QBFs. TCAD 26(3), 497–507 (2007)

    Google Scholar 

  17. Giunchiglia, E., Tacchella, A. (eds.): SAT 2003. LNCS, vol. 2919. Springer, Heidelberg (2004)

    Google Scholar 

  18. Goultiaeva, A., Iverson, V., Bacchus, F.: Beyond CNF: A Circuit-Based QBF Solver. In: Kullmann (ed.) [21], pp. 412–426

    Google Scholar 

  19. Pan, G., Vardi, M.Y.: Symbolic Decision Procedures for QBF. In: Wallace (ed.) [31], pp. 453–467

    Google Scholar 

  20. Jussila, T., Biere, A., Sinz, C., Kröning, D., Wintersteiger, C.M.: A First Step Towards a Unified Proof Checker for QBF. In: Marques-Silva, Sakallah (eds.) [25], pp. 201–214

    Google Scholar 

  21. Kullmann, O. (ed.): SAT 2009. LNCS, vol. 5584. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  22. Letz, R.: Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas. In: Egly, U., Fermüller, C.G. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, pp. 160–175. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Lonsing, F.: DepQBF 0.1 Source Code (2010), http://fmv.jku.at/depqbf/

  24. Lonsing, F., Biere, A.: A Compact Representation for Syntactic Dependencies in QBFs. In: Kullmann (ed.) [21], pp. 398–411

    Google Scholar 

  25. Marques-Silva, J., Sakallah, K.A. (eds.): SAT 2007. LNCS, vol. 4501. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  26. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: DAC 2001, pp. 530–535. ACM, New York (2001)

    Google Scholar 

  27. Samer, M.: Variable Dependencies of Quantified CSPs. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 512–527. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  28. Pigorsch, F., Scholl, C.: Exploiting structure in an AIG based QBF solver. In: DATE, pp. 1596–1601. IEEE, Los Alamitos (2009)

    Google Scholar 

  29. Pipatsrisawat, K., Darwiche, A.: A Lightweight Component Caching Scheme for Satisfiability Solvers. In: Marques-Silva, Sakallah (eds.) [25], pp. 294–299

    Google Scholar 

  30. Samer, M., Szeider, S.: Backdoor Sets of Quantified Boolean Formulas. Journal of Automated Reasoning (JAR) 42(1), 77–97 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wallace, M. (ed.): CP 2004. LNCS, vol. 3258. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  32. Zhang, L., Malik, S.: Conflict Driven Learning in a Quantified Boolean Satisfiability Solver. In: Pileggi, L.T., Kuehlmann, A. (eds.) ICCAD, pp. 442–449. ACM, New York (2002)

    Google Scholar 

  33. Zhang, L., Malik, S.: Towards a Symmetric 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 

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Authors and Affiliations

  1. Institute for Formal Models and Verification, Johannes Kepler University, Linz, Austria

    Florian Lonsing & Armin Biere

Authors
  1. Florian Lonsing
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  2. Armin Biere
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Editors and Affiliations

  1. Technion, Technion City, 32000, Haifa, Israel

    Ofer Strichman

  2. Vienna University of Technology, Favoritenstr. 9-11, 1040, Vienna, Austria

    Stefan Szeider

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Lonsing, F., Biere, A. (2010). Integrating Dependency Schemes in Search-Based QBF Solvers. In: Strichman, O., Szeider, S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14186-7_14

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  • DOI: https://doi.org/10.1007/978-3-642-14186-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14185-0

  • Online ISBN: 978-3-642-14186-7

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