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International Symposium on Automated Technology for Verification and Analysis

ATVA 2011: Automated Technology for Verification and Analysis pp 183–197Cite as

Antichain-Based QBF Solving

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6996))

Abstract

We consider the problem of QBF solving viewed as a reachability problem in an exponential And-Or graph. Antichain-based algorithms for reachability analysis in large graphs exploit certain subsumption relations to leverage the inherent structure of the explored graph in order to reduce the effect of state explosion, with high performance in practice.

In this paper, we propose simple notions of subsumption induced by the structural properties of the And-Or graphs for QBF solving. Subsumption is used to reduce the size of the search tree, and to define compact representations of certificates (in the form of antichains) both for positive and negative instances of QBF. We show that efficient exploration of the reduced search tree essentially relies on solving variants of Max-SAT and Min-SAT. Preliminary stand-alone experiments of this algorithm show that the antichain-based approach is promising.

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References

  1. Asano, T., Williamson, D.P.: Improved approximation algorithms for max sat. J. Algorithms 42(1), 173–202 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benedetti, M.: Evaluating QBFs via Symbolic Skolemization. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 285–300. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Benedetti, M.: Extracting Certificates from Quantified Boolean Formulas. In: Kaelbling, L.P., Saffiotti, A. (eds.) IJCAI, pp. 47–53. Professional Book Center (2005)

    Google Scholar 

  4. 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 

  5. Benedetti, M.: sKizzo: A Suite to Evaluate and Certify QBFs. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 369–376. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Benedetti, M., Mangassarian, H.: Qbf-based formal verification: Experience and perspectives. JSAT 5(1-4), 133–191 (2008)

    MathSciNet  MATH  Google Scholar 

  7. Biere, A.: PicoSAT Essentials. JSAT 4(2-4), 75–97 (2008)

    MATH  Google Scholar 

  8. Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate quantified Boolean formulae. In: Proc. of AAAI 1998/IAAI 1998, pp. 262–267. MIT Press, Cambridge (1998)

    Google Scholar 

  9. Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Cook, B., Kroening, D., Sharygina, N.: Verification of boolean programs with unbounded thread creation. Theor. Comput. Sci. 388(1-3), 227–242 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. De Wulf, M., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Antichains: A New Algorithm for Checking Universality of Finite Automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Doyen, L., Raskin, J.-F.: Antichain Algorithms for Finite Automata. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 2–22. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  13. Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving Advanced Reasoning Tasks Using Quantified Boolean Formulas. In: Proc. of IAAI, pp. 417–422. AAAI Press, Menlo Park (2000)

    Google Scholar 

  15. Giunchiglia, E., Narizzano, M., Tacchella, A.: Quantified Boolean Formulas satisfiability library (QBFLIB) (2001), www.qbflib.org

  16. Giunchiglia, E., Narizzano, M., Tacchella, A.: QuBE++: An Efficient QBF Solver. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 201–213. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  18. Jussila, T., Biere, A.: Compressing BMC Encodings with QBF. Electron. Notes Theor. Comput. Sci. 174, 45–56 (2007)

    Article  MATH  Google Scholar 

  19. Kohli, R., Krishnamurti, R., Mirchandani, P.: The Minimum Satisfiability Problem. SIAM J. Discrete Math. 7(2), 275–283 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kügel, A.: Improved Exact Solver for the Weighted Max-SAT problem. Accepted at the workshop Pragmatics of SAT. To appear in easychair electronic proceedings (2011)

    Google Scholar 

  21. Li, C.M., Manyà, F.: MaxSAT, Hard and Soft Constraints. In: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 613–631. IOS Press, Amsterdam (2009)

    Google Scholar 

  22. Lonsing, F., Biere, A.: DepQBF: A dependency-aware QBF solver (System Description). Journal on Satisfiability, Boolean Modeling and Computation 7, 71–76 (2010)

    Google Scholar 

  23. Lonsing, F., Biere, A.: Integrating Dependency Schemes in Search-Based QBF Solvers. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 158–171. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  24. Narizzano, M., Peschiera, C., Pulina, L., Tacchella, A.: Evaluating and certifying QBFs: A comparison of state-of-the-art tools. AI Commun. 22, 191–210 (2009)

    MathSciNet  MATH  Google Scholar 

  25. Pan, G., Vardi, M.Y.: Symbolic Decision Procedures for QBF. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 453–467. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  26. Papadimitriou, C.H.: Computational complexity. Addison-Wesley Publishing Company, Reading (1994)

    MATH  Google Scholar 

  27. Peschiera, C., Pulina, L., Tacchella, A., Bubeck, U., Kullmann, O., Lynce, I.: The Seventh QBF Solvers Evaluation (QBFEVAL 2010). In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 237–250. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  28. Samulowitz, H., Davies, J., Bacchus, F.: Preprocessing QBF. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 514–529. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut de Mathématique, Université de Mons, Belgique

    Thomas Brihaye & Marc Ducobu

  2. Institut d’Informatique, Université de Mons, Belgique

    Véronique Bruyère

  3. LSV, ENS Cachan & CNRS, France

    Laurent Doyen

  4. Département d’Informatique, Université Libre de Bruxelles, Belgique

    Jean-Francois Raskin

Authors
  1. Thomas Brihaye
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  2. Véronique Bruyère
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  3. Laurent Doyen
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  4. Marc Ducobu
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  5. Jean-Francois Raskin
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Editor information

Editors and Affiliations

  1. University of California, Santa Barbara, CA, USA

    Tevfik Bultan

  2. Department of Computer Science and Information Engineering, National Chung Cheng University, 168 University Road, Min-Hsiung, 62102, Chiayi, Taiwan, ROC

    Pao-Ann Hsiung

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Brihaye, T., Bruyère, V., Doyen, L., Ducobu, M., Raskin, JF. (2011). Antichain-Based QBF Solving. In: Bultan, T., Hsiung, PA. (eds) Automated Technology for Verification and Analysis. ATVA 2011. Lecture Notes in Computer Science, vol 6996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24372-1_14

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  • DOI: https://doi.org/10.1007/978-3-642-24372-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24371-4

  • Online ISBN: 978-3-642-24372-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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