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International Workshop on Programming Language Implementation and Logic Programming

PLILP 1990: Programming Language Implementation and Logic Programming pp 174–188Cite as

A new presburger arithmetic decision procedure based on extended prolog execution

  • Logic Programming
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 456))

Abstract

In this paper we are concerned by the problem of determining validity of universal Presburger formulas. The original point here is that we do not use a specific algorithm but attempt to prove Presburger formulas by induction using Kanamori et al.’ verification systems of extended Prolog execution. This leads us to a new decision algorithm for which a proof of correctness is given.

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References

  • Bledsoe, W.W. “A new method for proving certain Presburger formulas”, Advance Papers 4th Int. Joint Conf. on Artif. Intell., Tibilisi, 1975.

    Google Scholar 

  • Clark, K.L. “Predicate logic as a computational formalism”, Research Monograph: 79/59, TOC, Imperial College, 1979.

    Google Scholar 

  • Cooper, D.C. “Theorem proving in arithmetic without multiplication”. In Mach. Intell. 7, B. Meltzer and D. Michie, eds., American Elsevier, N.Y., 1972.

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  • Fribourg, L. “Equivalence-preserving transformations of inductive properties of Prolog programs”, Int. Conf. on Logic Programming, Seattle, 1988.

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  • Kanamori, T. and H. Fujita, “Formulation of induction formulas in verification of Prolog programs”, Conf. on Automated Deduction, Oxford, 1986.

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  • Kanamori, T. and H. Seki, “Verification of Prolog programs using an extension of execution”, Int. Conf. on Logic Programming, London, 1986.

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  • Shostak R. “On the SUP-INF method for proving Presburger formulas”, J. ACM 24:4, 1977.

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  • Suzuki, N. and D. Jefferson “Verification decidability of Presburger array programs”, J.ACM 27:1, 1980.

    Google Scholar 

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Author information

Authors and Affiliations

  1. L.I.E.N.S., 45 rue d'Ulm, 75005, Paris, France

    Laurent Fribourg

Authors
  1. Laurent Fribourg
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Editor information

Pierre Deransart Jan Maluszyński

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© 1990 Springer-Verlag Berlin Heidelberg

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Fribourg, L. (1990). A new presburger arithmetic decision procedure based on extended prolog execution. In: Deransart, P., Maluszyński, J. (eds) Programming Language Implementation and Logic Programming. PLILP 1990. Lecture Notes in Computer Science, vol 456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024184

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  • DOI: https://doi.org/10.1007/BFb0024184

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53010-7

  • Online ISBN: 978-3-540-46298-9

  • eBook Packages: Springer Book Archive

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