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On Preprocessing for Weighted MaxSAT

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12597))

Abstract

Modern competitive solvers employ various preprocessing techniques to efficiently tackle complex problems. This work introduces two preprocessing techniques to improve solving weighted partial MaxSAT problems: Generalized Boolean Multilevel Optimization (GBMO) and Trimming MaxSAT (TrimMaxSAT).

GBMO refines and extends Boolean Multilevel Optimization (BMO), thereby splitting instances due to their distribution of weights into multiple less complex subproblems, which are solved one after the other to obtain the overall solution.

The second technique, TrimMaxSAT, finds unsatisfiable soft clauses and removes them from the instance. This reduces the complexity of the MaxSAT instance and works especially well in combination with GBMO. The proposed algorithm works incrementally in a binary search fashion, testing the satisfiability of every soft clause. Furthermore, as a by-product, typically an initial weight close to the maximum is found, which is in turn advantageous w.r.t. the size of e.g. the Dynamic Polynomial Watchdog (DPW) encoding.

Both techniques can be used by all MaxSAT solvers, though our focus lies on Pseudo Boolean constraint based MaxSAT solvers. Experimental results show the effectiveness of both techniques on a large set of benchmarks from a hardware security application and from the 2019 MaxSAT Evaluation. In particular for the hardest of the application benchmarks, the solver Pacose with GBMO and TrimMaxSAT performs best compared to the MaxSAT Evaluation solvers of 2019. For the benchmarks of the 2019 MaxSAT Evaluation, we show that with the proposed techniques the top solver combination solves significantly more instances.

This work is supported by DFG project “Algebraic Fault Attacks” (BE 1176/20-2).

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Notes

  1. 1.

    QMaxSAT 2nd solver 2017 and Pacose 3rd solver 2018, same number of solved instances as 2nd MaxHS.

  2. 2.

    Available at the MaxSAT Evaluation 2020 [1].

  3. 3.

    These instances had weights bigger than the top weight.

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Authors and Affiliations

  1. Albert-Ludwigs-Universität Freiburg, Georges-Köhler-Allee 051, 79110, Freiburg im Breisgau, Germany

    Tobias Paxian, Pascal Raiola & Bernd Becker

Authors
  1. Tobias Paxian
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  2. Pascal Raiola
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  3. Bernd Becker
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Correspondence to Tobias Paxian .

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Editors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Fritz Henglein

  2. Tel Aviv University, Tel Aviv, Israel

    Sharon Shoham

  3. Technion, Haifa, Israel

    Yakir Vizel

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Paxian, T., Raiola, P., Becker, B. (2021). On Preprocessing for Weighted MaxSAT. In: Henglein, F., Shoham, S., Vizel, Y. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2021. Lecture Notes in Computer Science(), vol 12597. Springer, Cham. https://doi.org/10.1007/978-3-030-67067-2_25

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  • DOI: https://doi.org/10.1007/978-3-030-67067-2_25

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