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Non-prenex QBF Solving Using Abstraction

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Theory and Applications of Satisfiability Testing – SAT 2016 (SAT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9710))

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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/.

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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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