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International Conference on Theory and Applications of Satisfiability Testing

SAT 2005: Theory and Applications of Satisfiability Testing pp 241–256Cite as

A Scalable Method for Solving Satisfiability of Integer Linear Arithmetic Logic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3569))

Abstract

In this paper, we present a hybrid method for deciding problems involving integer and Boolean variables which is based on generic SAT solving techniques augmented with a) a polynomial-time ILP solver for the special class of Unit-Two-Variable-Per-Inequality (unit TVPI or UTVPI) constraints and b) an independent solver for general integer linear constraints. In our approach, we present a novel method for encoding linear constraints into the SAT solver through binary “indicator” variables. The hybrid SAT problem is subsequently solved using a SAT search procedure in close collaboration with the UTVPI solver. The UTVPI solver interacts closely with the Boolean SAT solver by passing implications and conflicting assignments. The non-UTVPI constraints are handled separately and participate in the learning scheme of the SAT solver through an innovative method based on the theory of cutting planes. Empirical evidence on software verification benchmarks is presented that demonstrates the advantages of our combined method.

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Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering and Computer Science, 1301 Beal Avenue, Ann Arbor, MI, 48109-2122, USA

    Hossein M. Sheini & Karem A. Sakallah

Authors
  1. Hossein M. Sheini
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  2. Karem A. Sakallah
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Toronto, Canada

    Fahiem Bacchus

  2. Dept. of Computer Science, Trinity College, Dublin 2

    Toby Walsh

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Sheini, H.M., Sakallah, K.A. (2005). A Scalable Method for Solving Satisfiability of Integer Linear Arithmetic Logic. In: Bacchus, F., Walsh, T. (eds) Theory and Applications of Satisfiability Testing. SAT 2005. Lecture Notes in Computer Science, vol 3569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499107_18

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  • DOI: https://doi.org/10.1007/11499107_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26276-3

  • Online ISBN: 978-3-540-31679-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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