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Polynomial-Time Validation of QCDCL Certificates

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Theory and Applications of Satisfiability Testing – SAT 2018 (SAT 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10929))

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Abstract

Quantified Boolean Formulas (QBFs) offer compact encodings of problems arising in areas such as verification and synthesis. These applications require that QBF solvers not only decide whether an input formula is true or false but also output a witnessing certificate, i.e. a representation of the winning strategy. State-of-the-art QBF solvers based on Quantified Conflict-Driven Constraint Learning (QCDCL) can emit Q-resolution proofs, from which in turn such certificates can be extracted. The correctness of a certificate generated in this way is validated by substituting it into the matrix of the input QBF and using a SAT solver to check that the resulting propositional formula (the validation formula) is unsatisfiable. This final check is often the most time-consuming part of the entire certification workflow. We propose a new validation method that does not require a SAT call and provably runs in polynomial time. It uses the Q-resolution proof from which the given certificate was extracted to directly generate a (propositional) proof of the validation formula in the RUP format, which can be verified by a proof checker such as DRAT-trim. Experiments with a prototype implementation show a robust, albeit modest, increase in the number of successfully validated certificates compared to validation with a SAT solver.

This research was partially supported by FWF grants P27721 and W1255-N23.

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Notes

  1. 1.

    We still have to make sure that the validation formula is constructed correctly so that it is not trivially unsatisfiable. We discuss this issue in Sect. 8.

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Authors and Affiliations

  1. Algorithms and Complexity Group, TU Wien, Vienna, Austria

    Tomáš Peitl, Friedrich Slivovsky & Stefan Szeider

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  1. Tomáš Peitl
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  2. Friedrich Slivovsky
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Correspondence to Friedrich Slivovsky .

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  1. Friedrich Schiller University Jena, Jena, Germany

    Olaf Beyersdorff

  2. Microsoft Research Ltd., Cambridge, United Kingdom

    Christoph M. Wintersteiger

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Peitl, T., Slivovsky, F., Szeider, S. (2018). Polynomial-Time Validation of QCDCL Certificates. In: Beyersdorff, O., Wintersteiger, C. (eds) Theory and Applications of Satisfiability Testing – SAT 2018. SAT 2018. Lecture Notes in Computer Science(), vol 10929. Springer, Cham. https://doi.org/10.1007/978-3-319-94144-8_16

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