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International Conference on Automated Deduction

CADE 2013: Automated Deduction – CADE-24 pp 215–230Cite as

Solving Difference Constraints over Modular Arithmetic

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7898))

Abstract

Difference logic is commonly used in program verification and analysis. In the context of fixed-precision integers, as used in assembly languages for example, the use of classical difference logic is unsound. We study the problem of deciding difference constraints in the context of modular arithmetic and show that it is strongly NP-complete. We discuss the applicability of the Bellman-Ford algorithm and related shortest-distance algorithms to the context of modular arithmetic. We explore two approaches, namely a complete method implemented using SMT technology and an incomplete fixpoint-based method, and the two are experimentally evaluated. The incomplete method performs considerably faster while maintaining acceptable accuracy on a range of instances.

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Author information

Authors and Affiliations

  1. Department of Computing and Information Systems, The University of Melbourne, Victoria, 3010, Australia

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

Authors
  1. Graeme Gange
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  2. Harald Søndergaard
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  3. Peter J. Stuckey
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  4. Peter Schachte
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Maria Paola Bonacina

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Gange, G., Søndergaard, H., Stuckey, P.J., Schachte, P. (2013). Solving Difference Constraints over Modular Arithmetic. In: Bonacina, M.P. (eds) Automated Deduction – CADE-24. CADE 2013. Lecture Notes in Computer Science(), vol 7898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38574-2_15

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  • DOI: https://doi.org/10.1007/978-3-642-38574-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38573-5

  • Online ISBN: 978-3-642-38574-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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