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DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

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Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional satisfiability (SAT) solvers. The Q-resolution calculus (QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0 implements a variant of QCDCL which is based on a generalization of QRES. This generalization is due to a set of additional axioms and leaves the original Q-resolution rules unchanged. The generalization of QRES enables QCDCL to potentially produce exponentially shorter proofs than the traditional variant. We present an overview of the features implemented in DepQBF and report on experimental results which demonstrate the effectiveness of generalized QRES in QCDCL.

Supported by the Austrian Science Fund (FWF) under grant S11409-N23.

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Notes

  1. 1.

    DepQBF is licensed under GPLv3: http://lonsing.github.io/depqbf/.

  2. 2.

    https://github.com/lonsing/nenofex.

  3. 3.

    We refer to an appendix of this paper with additional experimental results [30].

References

  1. Ayari, A., Basin, D.: 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). doi:10.1007/3-540-36126-X_12

    Chapter  Google Scholar 

  2. Balabanov, V., Jiang, J.R.: Unified QBF certification and its applications. Formal Methods Syst. Des. 41(1), 45–65 (2012)

    Article  MATH  Google Scholar 

  3. Balabanov, V., Widl, M., Jiang, J.-H.R.: QBF resolution systems and their proof complexities. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 154–169. Springer, Cham (2014). doi:10.1007/978-3-319-09284-3_12

    Google Scholar 

  4. Beyersdorff, O., Blinkhorn, J.: Dependency schemes in QBF calculi: semantics and soundness. In: Rueher, M. (ed.) CP 2016. LNCS, vol. 9892, pp. 96–112. Springer, Cham (2016). doi:10.1007/978-3-319-44953-1_7

    Chapter  Google Scholar 

  5. Beyersdorff, O., Chew, L., Janota, M.: Proof complexity of resolution-based QBF calculi. In: STACS. LIPIcs, vol. 30, pp. 76–89. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2015)

    Google Scholar 

  6. Biere, A.: Resolve and expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005). doi:10.1007/11527695_5

    Chapter  Google Scholar 

  7. Bogaerts, B., Janhunen, T., Tasharrofi, S.: SAT-to-SAT in QBFEval 2016. In: QBF Workshop. CEUR Workshop Proceedings, vol. 1719, pp. 63–70. CEUR-WS.org (2016)

    Google Scholar 

  8. 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). doi:10.1007/978-3-540-72788-0_24

    Chapter  Google Scholar 

  9. Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate quantified boolean formulae. In: AAAI, pp. 262–267. AAAI Press/The MIT Press (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), 752–794 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Davis, M., Logemann, G., Loveland, D.W.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  12. Egly, U., Kronegger, M., Lonsing, F., Pfandler, A.: Conformant planning as a case study of incremental QBF solving. Ann. Math. Artif. Intell. 80(1), 21–45 (2017)

    Article  MathSciNet  Google Scholar 

  13. Egly, U., Lonsing, F., Widl, M.: Long-distance resolution: proof generation and strategy extraction in search-based QBF solving. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR 2013. LNCS, vol. 8312, pp. 291–308. Springer, Heidelberg (2013). doi:10.1007/978-3-642-45221-5_21

    Chapter  Google Scholar 

  14. Giunchiglia, E., Narizzano, M., Tacchella, A.: Clause/Term resolution and learning in the evaluation of quantified boolean formulas. JAIR 26, 371–416 (2006)

    MathSciNet  MATH  Google Scholar 

  15. Heule, M., Järvisalo, M., Lonsing, F., Seidl, M., Biere, A.: Clause elimination for SAT and QSAT. JAIR 53, 127–168 (2015)

    MathSciNet  MATH  Google Scholar 

  16. Janota, M.: On Q-resolution and CDCL QBF solving. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 402–418. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_25

    Google Scholar 

  17. Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. Artif. Intell. 234, 1–25 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. Janota, M., Marques-Silva, J.: Expansion-based QBF solving versus Q-resolution. Theor. Comput. Sci. 577, 25–42 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Janota, M., Marques-Silva, J.: Solving QBF by clause selection. In: IJCAI, pp. 325–331. AAAI Press (2015)

    Google Scholar 

  20. Kleine Büning, H., Bubeck, U.: Theory of quantified boolean formulas. In: Handbook of Satisfiability, FAIA, vol. 185, pp. 735–760. IOS Press (2009)

    Google Scholar 

  21. Kleine Büning, H., Karpinski, M., Flögel, A.: Resolution for quantified boolean formulas. Inf. Comput. 117(1), 12–18 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  22. Klieber, W., Sapra, S., Gao, S., Clarke, E.: 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). doi:10.1007/978-3-642-14186-7_12

    Chapter  Google Scholar 

  23. Kullmann, O.: On a generalization of extended resolution. Discrete Appl. Math. 96–97, 149–176 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Letz, R.: Lemma and model caching in decision procedures for quantified boolean formulas. In: Egly, U., Fermüller, C.G. (eds.) TABLEAUX 2002. LNCS, vol. 2381, pp. 160–175. Springer, Heidelberg (2002). doi:10.1007/3-540-45616-3_12

    Chapter  Google Scholar 

  25. Lonsing, F., Bacchus, F., Biere, A., Egly, U., Seidl, M.: Enhancing search-based QBF solving by dynamic blocked clause elimination. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds.) LPAR 2015. LNCS, vol. 9450, pp. 418–433. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48899-7_29

    Chapter  Google Scholar 

  26. Lonsing, F., Biere, A.: DepQBF: a dependency-aware QBF solver. JSAT 7(2–3), 71–76 (2010)

    Google Scholar 

  27. 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). doi:10.1007/978-3-642-14186-7_14

    Chapter  Google Scholar 

  28. Lonsing, F., Egly, U.: Incremental QBF solving. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 514–530. Springer, Cham (2014). doi:10.1007/978-3-319-10428-7_38

    Google Scholar 

  29. Lonsing, F., Egly, U.: Incrementally computing minimal unsatisfiable cores of QBFs via a clause group solver API. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 191–198. Springer, Cham (2015). doi:10.1007/978-3-319-24318-4_14

    Chapter  Google Scholar 

  30. Lonsing, F., Egly, U.: DepQBF 6.0: A search-based QBF solver beyond traditional QCDCL. CoRR abs/1702.08256 (2017). http://arxiv.org/abs/1702.08256, CADE 2017 proceedings version with appendix

  31. Lonsing, F., Egly, U.: Evaluating QBF solvers: quantifier alternations matter. CoRR abs/1701.06612 (2017). http://arxiv.org/abs/1701.06612, technical report

  32. Lonsing, F., Egly, U., Seidl, M.: Q-resolution with generalized axioms. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 435–452. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_27

    Google Scholar 

  33. Lonsing, F., Egly, U., Van Gelder, A.: Efficient clause learning for quantified boolean formulas via QBF pseudo unit propagation. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 100–115. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39071-5_9

    Chapter  Google Scholar 

  34. Lonsing, F., Seidl, M., Van Gelder, A.: The QBF gallery: behind the scenes. Artif. Intell. 237, 92–114 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  35. Marin, P., Miller, C., Lewis, M.D.T., Becker, B.: Verification of partial designs using incremental QBF solving. In: DATE, pp. 623–628. IEEE (2012)

    Google Scholar 

  36. Marin, P., Narizzano, M., Pulina, L., Tacchella, A., Giunchiglia, E.: Twelve years of QBF evaluations: QSAT is PSPACE-hard and it shows. Fundam. Inform. 149(1–2), 133–158 (2016)

    Article  MathSciNet  Google Scholar 

  37. Niemetz, A., Preiner, M., Lonsing, F., Seidl, M., Biere, A.: Resolution-based certificate extraction for QBF. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 430–435. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31612-8_33

    Chapter  Google Scholar 

  38. Peitl, T., Slivovsky, F., Szeider, S.: Long distance Q-resolution with dependency schemes. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 500–518. Springer, Cham (2016). doi:10.1007/978-3-319-40970-2_31

    Google Scholar 

  39. Pulina, L.: The ninth QBF solvers evaluation - preliminary report. In: Proceedings of the 4th International Workshop on Quantified Boolean Formulas QBF 2016. CEUR Workshop Proceedings, vol. 1719, pp. 1–13. CEUR-WS.org (2016)

  40. Rabe, M.N., Tentrup, L.: CAQE: a certifying QBF solver. In: FMCAD, pp. 136–143. IEEE (2015)

    Google Scholar 

  41. Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. ACM 12(1), 23–41 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  42. Samer, M., Szeider, S.: Backdoor sets of quantified boolean formulas. JAR 42(1), 77–97 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  43. Scholl, C., Pigorsch, F.: The QBF solver AIGSolve. In: QBF Workshop. CEUR Workshop Proceedings, vol. 1719, pp. 55–62. CEUR-WS.org (2016)

    Google Scholar 

  44. Marques-Silva, J., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Handbook of Satisfiability, FAIA, vol. 185, pp. 131–153. IOS Press (2009)

    Google Scholar 

  45. Slivovsky, F., Szeider, S.: Computing resolution-path dependencies in linear time. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 58–71. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31612-8_6

    Chapter  Google Scholar 

  46. Slivovsky, F., Szeider, S.: Soundness of Q-resolution with dependency schemes. Theor. Comput. Sci. 612, 83–101 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  47. Van Gelder, A.: Variable independence and resolution paths for quantified boolean formulas. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 789–803. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23786-7_59

    Chapter  Google Scholar 

  48. Van Gelder, A.: Contributions to the theory of practical quantified boolean formula solving. In: Milano, M. (ed.) CP 2012. LNCS, pp. 647–663. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33558-7_47

    Chapter  Google Scholar 

  49. Zhang, L., Malik, S.: Conflict driven learning in a quantified boolean satisfiability solver. In: ICCAD, pp. 442–449. ACM/IEEE Computer Society (2002)

    Google Scholar 

  50. Zhang, L., Malik, S.: Towards a symmetric treatment of satisfaction and conflicts in quantified boolean formula evaluation. In: Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 200–215. Springer, Heidelberg (2002). doi:10.1007/3-540-46135-3_14

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Knowledge-Based Systems Group, Vienna University of Technology, Vienna, Austria

    Florian Lonsing & Uwe Egly

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  1. Florian Lonsing
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  2. Uwe Egly
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Correspondence to Florian Lonsing .

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  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Lonsing, F., Egly, U. (2017). DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_23

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