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A Cube Distribution Approach to QBF Solving and Certificate Minimization

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Principles and Practice of Constraint Programming (CP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11802))

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Abstract

Quantified Boolean Formulas (QBFs) are powerful expressions to naturally and concisely encode many decision problems in computer science, such as robotic planning, hardware/software synthesis and verification, among others. Their effective solving and certificate (in terms of model and countermodel) generation play crucial roles to enable practical applications. In this work, we give a new view on QBF solving and certificate generation by the cube distribution interpretation. It provides a largely increased flexibility for QBF reasoning and allows compact certificate derivation with don’t cares. Through this interpretation, we develop a QBF solver based on the prior clause selection framework. Experimental results demonstrate the superiority of our solver in both solving performance and certificate size compared to other state-of-the-art solvers with certificate generation ability.

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Notes

  1. 1.

    In fact, bloqqer [3] cannot directly solve the formula with all options being enabled, except for three options: covered clause elimination, variable elimination, and universal expansion. Disabling these three options is reasonable in that (1) covered clause elimination often considerably increases the size of the Skolem functions as discussed in [8], (2) variable elimination in principle can solve all QBFs, and (3) universal expansion in principle reduces all QBFs to SAT.

  2. 2.

    As QBFEVAL’16 contains more benchmark instances than QBFEVAL’17 and QBFEVAL’18, we took QBFEVAL’16 benchmarks for our experimental study.

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Acknowledgment

The authors thank Mikolas Janota for providing the Qesto source code. This work was supported in part by the Ministry of Science and Technology of Taiwan under grants 105-2221-E-002-196-MY3, 105-2923-E-002-016-MY3, and 108-2221-E-002-144-MY3.

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Authors and Affiliations

  1. Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, 10617, Taiwan

    Li-Cheng Chen & Jie-Hong R. Jiang

  2. Department of Electrical Engineering, National Taiwan University, Taipei, 10617, Taiwan

    Jie-Hong R. Jiang

Authors
  1. Li-Cheng Chen
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  2. Jie-Hong R. Jiang
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Correspondence to Jie-Hong R. Jiang .

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Editors and Affiliations

  1. INRA, Castanet Tolosan, France

    Thomas Schiex

  2. INRA, Castanet Tolosan, France

    Simon de Givry

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Chen, LC., Jiang, JH.R. (2019). A Cube Distribution Approach to QBF Solving and Certificate Minimization. In: Schiex, T., de Givry, S. (eds) Principles and Practice of Constraint Programming. CP 2019. Lecture Notes in Computer Science(), vol 11802. Springer, Cham. https://doi.org/10.1007/978-3-030-30048-7_31

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  • DOI: https://doi.org/10.1007/978-3-030-30048-7_31

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  • Online ISBN: 978-3-030-30048-7

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