Skip to main content
SpringerLink
Log in

Solving QBF with Counterexample Guided Refinement

  • Conference paper
Theory and Applications of Satisfiability Testing – SAT 2012 (SAT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7317))

Abstract

We propose two novel approaches for using Counterexample-Guided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an additional learning technique in an existing DPLL-based QBF solver. Experimental evaluation of the implemented prototypes shows that the CEGAR-driven solver outperforms existing solvers on a number of families in the QBF-LIB and that the DPLL solver benefits from the additional type of learning. Thus this article opens two promising avenues in QBF: CEGAR-driven solvers as an alternative to existing approaches and a novel type of learning in DPLL.

This work is partially supported by FCT grants ATTEST (CMU-PT/ELE/0009/2009) and POLARIS (PTDC/EIA-CCO/123051/2010), by SFI grant BEACON (09/IN.1/I2618), and by Semiconductor Research Corporation contract 2005TJ1366.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Chapter  Google Scholar 

  2. Barrett, C.W., Dill, D.L., Stump, A.: Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 236–249. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. 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 

  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. Biere, A., Lonsing, F., Seidl, M.: Blocked Clause Elimination for QBF. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 101–115. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Browning, B., Remshagen, A.: A SAT-based solver for Q-ALL SAT. In: ACM Southeast Regional Conference (2006)

    Google Scholar 

  7. Bubeck, U., Kleine Büning, H.: Bounded Universal Expansion for Preprocessing QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 244–257. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Büning, H.K., Bubeck, U.: Theory of quantified boolean formulas. In: Handbook of Satisfiability. IOS Press (2009)

    Google Scholar 

  9. Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate Quantified Boolean Formulae. In: National Conference on Artificial Intelligence (1998)

    Google Scholar 

  10. Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5) (2003)

    Google Scholar 

  11. 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 

  12. Giunchiglia, E., Marin, P., Narizzano, M.: QuBE 7.0 system description. Journal on Satisfiability, Boolean Modeling and Computation 7 (2010)

    Google Scholar 

  13. Giunchiglia, E., Marin, P., Narizzano, M.: Reasoning with quantified boolean formulas. In: Handbook of Satisfiability. IOS Press (2009)

    Google Scholar 

  14. Giunchiglia, E., Marin, P., Narizzano, M.: sQueezeBF: An Effective Preprocessor for QBFs Based on Equivalence Reasoning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 85–98. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Goultiaeva, A., Bacchus, F.: Exploiting QBF duality on a circuit representation. In: AAAI (2010)

    Google Scholar 

  16. Janota, M., Grigore, R., Marques-Silva, J.: Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS, vol. 6341, pp. 195–207. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Janota, M., Marques-Silva, J.: Abstraction-Based Algorithm for 2QBF. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 230–244. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Klieber, W., Sapra, S., Gao, S., Clarke, E.M.: A Non-prenex, Non-clausal QBF Solver with Game-State Learning. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 128–142. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Lonsing, F., Biere, A.: Nenofex: Expanding NNF for QBF Solving. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 196–210. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Lonsing, F., Biere, A.: DepQBF: A dependency-aware QBF solver. JSAT (2010)

    Google Scholar 

  21. Lonsing, F., Biere, A.: Failed Literal Detection for QBF. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 259–272. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  22. Mneimneh, M., Sakallah, K.: Computing Vertex Eccentricity in Exponentially Large Graphs: QBF Formulation and Solution. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 411–425. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  23. Monniaux, D.: Quantifier Elimination by Lazy Model Enumeration. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 585–599. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  24. de Moura, L., Rueß, H., Sorea, M.: Lazy Theorem Proving for Bounded Model Checking over Infinite Domains. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 438–455. Springer, Heidelberg (2002)

    Google Scholar 

  25. The Quantified Boolean Formulas satisfiability library, http://www.qbflib.org/

  26. Samulowitz, H., Bacchus, F.: Using SAT in QBF. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 578–592. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  27. Wintersteiger, C.M., Hamadi, Y., de Moura, L.: Efficiently Solving Quantified Bit-Vector Formulas. In: FMCAD (2010)

    Google Scholar 

  28. Zhang, L., Malik, S.: Conflict driven learning in a quantified Boolean satisfiability solver. In: ICCAD (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IST/INESC-ID, Lisbon, Portugal

    Mikoláš Janota & Joao Marques-Silva

  2. University College Dublin, Ireland

    Joao Marques-Silva

  3. Carnegie Mellon University, Pittsburgh, PA, USA

    William Klieber & Edmund Clarke

Authors
  1. Mikoláš Janota
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Klieber
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joao Marques-Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Edmund Clarke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Center for Information Technology, Fondazione Bruno Kessler, via Sommarive 18, Povo, 38123, Trento, Italy

    Alessandro Cimatti

  2. Department of Information Engineering and Computer Science, University of Trento, via Sommarive 14, Povo, 38123, Trento, Italy

    Roberto Sebastiani

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Janota, M., Klieber, W., Marques-Silva, J., Clarke, E. (2012). Solving QBF with Counterexample Guided Refinement. In: Cimatti, A., Sebastiani, R. (eds) Theory and Applications of Satisfiability Testing – SAT 2012. SAT 2012. Lecture Notes in Computer Science, vol 7317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31612-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31612-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31611-1

  • Online ISBN: 978-3-642-31612-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation