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Short Proofs Without New Variables

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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

Adding and removing redundant clauses is at the core of state-of-the-art SAT solving. Crucial is the ability to add short clauses whose redundancy can be determined in polynomial time. We present a characterization of the strongest notion of clause redundancy (i.e., addition of the clause preserves satisfiability) in terms of an implication relationship. By using a polynomial-time decidable implication relation based on unit propagation, we thus obtain an efficiently checkable redundancy notion. A proof system based on this notion is surprisingly strong, even without the introduction of new variables—the key component of short proofs presented in the proof complexity literature. We demonstrate this strength on the famous pigeon hole formulas by providing short clausal proofs without new variables.

This work has been supported by the National Science Foundation under grant CCF-1526760 and the Austrian Science Fund (FWF) under project W1255-N23.

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Notes

  1. 1.

    The checker, benchmark formulas, and proofs are available at http://www.cs.utexas.edu/~marijn/pr/.

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Author information

Authors and Affiliations

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

    Marijn J. H. Heule

  2. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Benjamin Kiesl

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

    Armin Biere

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

Correspondence to Marijn J. H. Heule .

Editor information

Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Heule, M.J.H., Kiesl, B., Biere, A. (2017). Short Proofs Without New Variables. 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_9

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  • DOI: https://doi.org/10.1007/978-3-319-63046-5_9

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