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Compositional Propositional Proofs

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2015)

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Abstract

Many hard-combinatorial problems have only be solved by SAT solvers in a massively parallel setting. This reduces the trust one has in the final result as errors might occur during parallel SAT solving or during partitioning of the original problem. We present a new framework to produce clausal proofs for cube-and-conquer, arguably the most effective parallel SAT solving paradigm for hard-combinatorial problems. The framework also provides an elegant approach to parallelize the validation of clausal proofs efficiently, both in terms of run time and memory usage. We evaluate the presented approach on some hard-combinatorial problems and validate constructed clausal proofs in parallel.

This work was supported by the Austrian Science Fund (FWF) through the national research network RiSE (S11408-N23), DARPA contract number N66001-10-2-4087, and the National Science Foundation under grant number CCF-1526760.

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Notes

  1. 1.

    All solver techniques can be expressed as a RAT derivation. For some techniques, such as symmetry-breaking, the construction of a RAT derivation is complex [20].

  2. 2.

    see http://www.siert.nl/icnf/ for details.

  3. 3.

    available on http://www.cs.utexas.edu/~marijn/sbp/.

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Acknowledgements

The authors thank Nathan Wetzler for his helpful comments to improve the paper and acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing grid resources that have contributed to the research results reported within this paper.

Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Texas, Austin, USA

    Marijn J. H. Heule

  2. Institute for Formal Models and Verification, JKU, Linz, Austria

    Armin Biere

Authors
  1. Marijn J. H. Heule
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  2. Armin Biere
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Corresponding author

Correspondence to Marijn J. H. Heule .

Editor information

Editors and Affiliations

  1. New York University, New York, New York, USA

    Martin Davis

  2. University of the South Pacific, Suva, Fiji

    Ansgar Fehnker

  3. Macquarie University, Sydney, New South Wales, Australia

    Annabelle McIver

  4. The University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

A Proof-Logging Bug in CDCL Solvers

A Proof-Logging Bug in CDCL Solvers

We observed a bug in the clausal proof logging of Glucose version 3.0, which actually occurs in all MiniSAT-based solvers — which is the majority of state-of-the-art solvers these days. The bug consists of deleting pseudo-unit clauses. This bug can simply be fixed by adding the following lines to Solver.cc:

figure a

just below the beginning of the removeClause procedure

figure b

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Heule, M.J.H., Biere, A. (2015). Compositional Propositional Proofs. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_31

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  • DOI: https://doi.org/10.1007/978-3-662-48899-7_31

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