Non-prenex QBF Solving Using Abstraction

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9710)

Abstract

In a recent work, we introduced an abstraction based algorithm for solving quantified Boolean formulas (QBF) in prenex negation normal form (PNNF) where quantifiers are only allowed in the formula’s prefix and negation appears only in front of variables. In this paper, we present a modified algorithm that lifts the restriction on prenex quantifiers. Instead of a linear quantifier prefix, the algorithm handles tree-shaped quantifier hierarchies where different branches can be solved independently. In our implementation, we exploit this property by solving independent branches in parallel. We report on an evaluation of our implementation on a recent case study regarding the synthesis of finite-state controllers from \(\omega \)-regular specifications.

References

  1. 1.
    Biere, A.: PicoSAT essentials. JSAT 4(2–4), 75–97 (2008)MATHGoogle Scholar
  2. 2.
    Bohy, A., Bruyère, V., Filiot, E., Jin, N., Raskin, J.-F.: Acacia+, a tool for LTL synthesis. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 652–657. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Egly, U., Seidl, M., Woltran, S.: A solver for QBFs in negation normal form. Constraints 14(1), 38–79 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Faymonville, P., Finkbeiner, B., Rabe, M.N., Tentrup, L.: Encodings of reactive synthesis. In: Proceedings of QUANTIFY (2015)Google Scholar
  5. 5.
    Finkbeiner, B., Schewe, S.: Bounded synthesis. STTT 15(5–6), 519–539 (2013)CrossRefMATHGoogle Scholar
  6. 6.
    Goultiaeva, A., Iverson, V., Bacchus, F.: Beyond CNF: a circuit-based QBF solver. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 412–426. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Janota, M., Klieber, W., Marques-Silva, J., Clarke, E.: Solving QBF with counterexample guided refinement. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 114–128. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Janota, M., Marques-Silva, J.: Solving QBF by clause selection. In: Proceedings of IJCAI, pp. 325–331. AAAI Press (2015)Google Scholar
  9. 9.
    Jordan, C., Kaiser, L., Lonsing, F., Seidl, M.: MPIDepQBF: towards parallel QBF solving without knowledge sharing. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 430–437. Springer, Heidelberg (2014)Google Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Lewis, M.D.T., Schubert, T., Becker, B.: QmiraXT - a multithreaded QBF solver. In: Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen (MBMV), Berlin, Germany, 2–4 March 2009, pp. 7–16. Universitätsbibliothek Berlin, Germany (2009)Google Scholar
  12. 12.
    Lewis, M.D.T., Schubert, T., Becker, B., Marin, P., Narizzano, M., Giunchiglia, E.: Parallel QBF solving with advanced knowledge sharing. Fundam. Inf. 107(2–3), 139–166 (2011)MathSciNetGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Mota, B.D., Nicolas, P., Stéphan, I.: A new parallel architecture for QBF tools. In: Proceedings of HPCS, pp. 324–330. IEEE (2010)Google Scholar
  15. 15.
    Pigorsch, F., Scholl, C.: Exploiting structure in an AIG based QBF solver. In: Proceedings of DATE, pp. 1596–1601. IEEE (2009)Google Scholar
  16. 16.
    QBF Gallery 2014: QCIR-G14: a non-prenex non-CNF format for quantified Boolean formulas. http://qbf.satisfiability.org/gallery/qcir-gallery14.pdf
  17. 17.
    Rabe, M.N., Tentrup, L.: CAQE: a certifying QBF solver. In: Proceedings of FMCAD, pp. 136–143. IEEE (2015)Google Scholar
  18. 18.
    Tentrup, L.: Solving QBF by abstraction. CoRR abs/1604.06752 (2016). https://arxiv.org/abs/1604.06752
  19. 19.
    Tu, K.-H., Hsu, T.-C., Jiang, J.-H.R.: QELL: QBF reasoning with extended clause learning and levelized SAT solving. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 343–359. Springer, Heidelberg (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Reactive Systems GroupSaarland UniversitySaarbrückenGermany

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