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International Conference on Theory and Applications of Satisfiability Testing

SAT 2016: Theory and Applications of Satisfiability Testing – SAT 2016 pp 393–401Cite as

Non-prenex QBF Solving Using Abstraction

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This work was partially supported by the German Research Foundation (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).

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Notes

  1. 1.

    Available at https://www.react.uni-saarland.de/tools/quabs/.

References

  1. Biere, A.: PicoSAT essentials. JSAT 4(2–4), 75–97 (2008)

    MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  3. Egly, U., Seidl, M., Woltran, S.: A solver for QBFs in negation normal form. Constraints 14(1), 38–79 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Faymonville, P., Finkbeiner, B., Rabe, M.N., Tentrup, L.: Encodings of reactive synthesis. In: Proceedings of QUANTIFY (2015)

    Google Scholar 

  5. Finkbeiner, B., Schewe, S.: Bounded synthesis. STTT 15(5–6), 519–539 (2013)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

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

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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)

    MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  18. Tentrup, L.: Solving QBF by abstraction. CoRR abs/1604.06752 (2016). https://arxiv.org/abs/1604.06752

  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)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Reactive Systems Group, Saarland University, Saarbrücken, Germany

    Leander Tentrup

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  1. Leander Tentrup
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Correspondence to Leander Tentrup .

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Editors and Affiliations

  1. Aix-Marseille Université, Marseille, France

    Nadia Creignou

  2. Université d'Artois, Lens, France

    Daniel Le Berre

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Tentrup, L. (2016). Non-prenex QBF Solving Using Abstraction. In: Creignou, N., Le Berre, D. (eds) Theory and Applications of Satisfiability Testing – SAT 2016. SAT 2016. Lecture Notes in Computer Science(), vol 9710. Springer, Cham. https://doi.org/10.1007/978-3-319-40970-2_24

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  • DOI: https://doi.org/10.1007/978-3-319-40970-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40969-6

  • Online ISBN: 978-3-319-40970-2

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