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Efficient Verified (UN)SAT Certificate Checking

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Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

We present an efficient formally verified checker for satisfiability and unsatisfiability certificates for Boolean formulas in conjunctive normal form. It utilizes a two phase approach: Starting from a DRAT certificate, the unverified generator computes an enriched certificate, which is checked against the original formula by the verified checker.

Using the Isabelle/HOL Refinement Framework, we verify the actual implementation of the checker, specifying the semantics of the formula down to the integer sequence that represents it.

On a realistic benchmark suite drawn from the 2016 SAT competition, our approach is more than two times faster than the unverified standard tool drat-trim. Additionally, we implemented a multi-threaded version of the generator, which further reduces the runtime.

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Notes

  1. 1.

    Unfortunately, the available version history of drat-trim [9] only dates back to October 2016. We can only speculate whether the discovered bugs were present in the versions used for the 2014 and 2016 SAT competitions.

  2. 2.

    However, we expect that most of our optimizations can be transferred to their tools.

  3. 3.

    Our profiling data indicates that, depending on the problem, up to 93% of the time is spent for unit propagation.

  4. 4.

    Blocked lemmas are useless for unsat proofs, such that there is no point to include them into the certificate.

  5. 5.

    The name suffix instead of indicates that the data structure may be stored on the heap.

  6. 6.

    Element 0 is used as a guard in our implementation.

  7. 7.

    The current version at the time of writing this paper.

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Acknowledgements

We thank Jasmin Blanchette and Mathias Fleury for very useful comments on the draft version of this paper, and Lars Hupel for instant help on any problems related to the benchmark server.

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  1. Technische Universität München, Munich, Germany

    Peter Lammich

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Correspondence to Peter Lammich .

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  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Lammich, P. (2017). Efficient Verified (UN)SAT Certificate Checking. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_15

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