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Linear Integer Arithmetic Revisited

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Automated Deduction - CADE-25 (CADE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

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Abstract

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect termination in favor of efficiency. It is challenging to design a solver that is both terminating and practically efficient. Recent work by Jovanović and de Moura constitutes an important step into this direction. Their algorithm CUTSAT is sound, but does not terminate, in general. In this paper we extend their CUTSAT algorithm by refined inference rules, a new type of conflicting core, and a dedicated rule application strategy. This leads to our algorithm CUTSAT++, which guarantees termination.

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Notes

  1. 1.

    The restrictions to maximal variables in the definition of conflicting cores and to the Solve-Div rule were both confirmed as missing but necessary in a private communication with Jovanović.

  2. 2.

    As recommended in [8], CUTSAT++ uses the same slack variable for all Slack-Intro applications.

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Acknowledgments

This research was supported in part by the German Transregional Collaborative Research Center SFB/TR 14 AVACS and by the ANR/DFG project STU 483/2-1 SMArT.

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Authors and Affiliations

  1. Max Planck Institute for Informatics, Saarbrücken, Germany

    Martin Bromberger, Thomas Sturm & Christoph Weidenbach

Authors
  1. Martin Bromberger
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  2. Thomas Sturm
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  3. Christoph Weidenbach
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Corresponding author

Correspondence to Martin Bromberger .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Bromberger, M., Sturm, T., Weidenbach, C. (2015). Linear Integer Arithmetic Revisited. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_42

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_42

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

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