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DRMaxSAT with MaxHS: First Contact

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Theory and Applications of Satisfiability Testing – SAT 2019 (SAT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11628))

Abstract

The proof system of Dual-Rail MaxSAT (DRMaxSAT) was recently shown to be capable of efficiently refuting families of formulas that are well-known to be hard for resolution, concretely when the MaxSAT solving approach is either MaxSAT resolution or core-guided algorithms. Moreover, DRMaxSAT based on MaxSAT resolution was shown to be stronger than general resolution. Nevertheless, existing experimental evidence indicates that the use of MaxSAT algorithms based on the computation of minimum hitting sets (MHSes), i.e. MaxHS-like algorithms, are as effective, and often more effective, than core-guided algorithms and algorithms based on MaxSAT resolution. This paper investigates the use of MaxHS-like algorithms in the DRMaxSAT proof system. Concretely, the paper proves that the propositional encoding of the pigenonhole and doubled pigenonhole principles have polynomial time refutations when the DRMaxSAT proof system uses a MaxHS-like algorithm.

This work was supported by FCT grants ABSOLV (PTDC/CCI-COM/28986/2017), FaultLocker (PTDC/CCI-COM/29300/2017), SAFETY (SFRH/BPD/120315/2016), and SAMPLE (CEECIND/04549/2017); grant TIN2016-76573-C2-2-P (TASSAT 3); and Simons Foundation grant 578919.

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Notes

  1. 1.

    Despite ongoing efforts, and with the exception of families of problem instances known to be hard for resolution, the performance of implementations of proof systems stronger than resolution is still far from what CDCL SAT solvers achieve in practice.

  2. 2.

    The plots show the performance of the competitors for a specifically constructed PHP and 2PHP formulas, with \({\mathcal {P}}\) clauses being disabled. (The notation and rationale will be explained below. A reader can also refer to [9, 20] for details.)

  3. 3.

    Some of the (2)PHP instances are skipped in the plots. Please, refer to [9, 20] for details.

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Author information

Authors and Affiliations

  1. Faculty of Science, University of Lisbon, Lisbon, Portugal

    Antonio Morgado, Alexey Ignatiev & Joao Marques-Silva

  2. Computer Science, Universidad Politécnica de Cataluña, Barcelona, Spain

    Maria Luisa Bonet

  3. Department of Mathematics, University of California, San Diego, USA

    Sam Buss

  4. ISDCT SB RAS, Irkutsk, Russia

    Alexey Ignatiev

Authors
  1. Antonio Morgado
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  2. Alexey Ignatiev
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  3. Maria Luisa Bonet
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  4. Joao Marques-Silva
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  5. Sam Buss
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Corresponding author

Correspondence to Antonio Morgado .

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Editors and Affiliations

  1. University of Lisbon, Lisbon, Portugal

    Mikoláš Janota

  2. University of Lisbon, Lisbon, Portugal

    Inês Lynce

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Morgado, A., Ignatiev, A., Bonet, M.L., Marques-Silva, J., Buss, S. (2019). DRMaxSAT with MaxHS: First Contact. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham. https://doi.org/10.1007/978-3-030-24258-9_17

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  • DOI: https://doi.org/10.1007/978-3-030-24258-9_17

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