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International Conference on Theory and Applications of Satisfiability Testing

SAT 2017: Theory and Applications of Satisfiability Testing – SAT 2017 pp 380–397Cite as

A Benders Decomposition Approach to Deciding Modular Linear Integer Arithmetic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10491))

Abstract

Verification tasks frequently require deciding systems of linear constraints over modular (machine) arithmetic. Existing approaches for reasoning over modular arithmetic use bit-vector solvers, or else approximate machine integers with mathematical integers and use arithmetic solvers. Neither is ideal; the first is sound but inefficient, and the second is efficient but unsound. We describe a linear encoding which correctly describes modular arithmetic semantics, yielding an optimistic but sound approach. Our method abstracts the problem with linear arithmetic, but progressively refines the abstraction when modular semantics is violated. This preserves soundness while exploiting the mostly integer nature of the constraint problem. We present a prototype implementation, which gives encouraging experimental results.

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Acknowledgments

We are grateful for support from the Australian Research Council. The work has been supported by Discovery Project grant DP140102194, and Graeme Gange is supported through Discovery Early Career Researcher Award DE160100568.

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Authors and Affiliations

  1. School of Computing and Information Systems, The University of Melbourne, Melbourne, VIC, 3010, Australia

    Bishoksan Kafle, Graeme Gange, Peter Schachte, Harald Søndergaard & Peter J. Stuckey

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  1. Bishoksan Kafle
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  2. Graeme Gange
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Correspondence to Bishoksan Kafle .

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  1. UNSW Sydney, Sydney, New South Wales, Australia

    Serge Gaspers

  2. University of New South Wales , Sydney, New South Wales, Australia

    Toby Walsh

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Kafle, B., Gange, G., Schachte, P., Søndergaard, H., Stuckey, P.J. (2017). A Benders Decomposition Approach to Deciding Modular Linear Integer Arithmetic. In: Gaspers, S., Walsh, T. (eds) Theory and Applications of Satisfiability Testing – SAT 2017. SAT 2017. Lecture Notes in Computer Science(), vol 10491. Springer, Cham. https://doi.org/10.1007/978-3-319-66263-3_24

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  • DOI: https://doi.org/10.1007/978-3-319-66263-3_24

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