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International Conference on Tools and Algorithms for the Construction and Analysis of Systems

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Clausal Proofs for Pseudo-Boolean Reasoning

Clausal Proofs for Pseudo-Boolean Reasoning

  • Randal E. Bryant  ORCID: orcid.org/0000-0001-5024-661310,
  • Armin Biere  ORCID: orcid.org/0000-0001-7170-924211 &
  • Marijn J. H. Heule  ORCID: orcid.org/0000-0002-5587-880110 
  • Conference paper
  • Open Access
  • First Online: 30 March 2022

  • 2618 Accesses

Part of the Lecture Notes in Computer Science book series (LNCS,volume 13243)

Abstract

When augmented with a Pseudo-Boolean (PB) solver, a Boolean satisfiability (SAT) solver can apply apply powerful reasoning methods to determine when a set of parity or cardinality constraints, extracted from the clauses of the input formula, has no solution. By converting the intermediate constraints generated by the PB solver into ordered binary decision diagrams (BDDs), a proof-generating, BDD-based SAT solver can then produce a clausal proof that the input formula is unsatisfiable. Working together, the two solvers can generate proofs of unsatisfiability for problems that are intractable for other proof-generating SAT solvers. The PB solver can, at times, detect that the proof can exploit modular arithmetic to give smaller BDD representations and therefore shorter proofs.

The first and third authors were supported by the U. S. National Science Foundation under grant CCF-2108521

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, United States

    Randal E. Bryant & Marijn J. H. Heule

  2. Albert-Ludwigs University, Freiburg, Germany

    Armin Biere

Authors
  1. Randal E. Bryant
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  2. Armin Biere
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  3. Marijn J. H. Heule
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Corresponding author

Correspondence to Randal E. Bryant .

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Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be'er Sheva, Israel

    Dr. Dana Fisman

  2. University of Illinois Urbana-Champaign, Urbana, IL, USA

    Grigore Rosu

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Bryant, R.E., Biere, A., Heule, M.J.H. (2022). Clausal Proofs for Pseudo-Boolean Reasoning. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13243. Springer, Cham. https://doi.org/10.1007/978-3-030-99524-9_25

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  • DOI: https://doi.org/10.1007/978-3-030-99524-9_25

  • Published: 30 March 2022

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