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.
Preview
Unable to display preview. Download preview PDF.
References
Bledsoe, W.W. “A new method for proving certain Presburger formulas”, Advance Papers 4th Int. Joint Conf. on Artif. Intell., Tibilisi, 1975.
Clark, K.L. “Predicate logic as a computational formalism”, Research Monograph: 79/59, TOC, Imperial College, 1979.
Cooper, D.C. “Theorem proving in arithmetic without multiplication”. In Mach. Intell. 7, B. Meltzer and D. Michie, eds., American Elsevier, N.Y., 1972.
Fribourg, L. “Equivalence-preserving transformations of inductive properties of Prolog programs”, Int. Conf. on Logic Programming, Seattle, 1988.
Kanamori, T. and H. Fujita, “Formulation of induction formulas in verification of Prolog programs”, Conf. on Automated Deduction, Oxford, 1986.
Kanamori, T. and H. Seki, “Verification of Prolog programs using an extension of execution”, Int. Conf. on Logic Programming, London, 1986.
Shostak R. “On the SUP-INF method for proving Presburger formulas”, J. ACM 24:4, 1977.
Suzuki, N. and D. Jefferson “Verification decidability of Presburger array programs”, J.ACM 27:1, 1980.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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