Craig Interpolation for Quantifier-Free Presburger Arithmetic

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Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinite-state systems. They also help improve the refinement of iteratively computed lazy abstractions. Efficient interpolation procedures have been presented only for a few theories. In this paper, we introduce a complete interpolation method for the full range of quantifier-free Presburger arithmetic formulas. We propose a novel convex variable projection for integer inequalities and a technique to combine them with equalities. The derivation of the interpolant has complexity low-degree polynomial in the size of the refutation proof and is typically fast in practice.
15 pages, 1 algorithm, 1 figure

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Logic in Computer Science, Symbolic Computation

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http://salesiana.dossiersoluciones.com/handle/123456789/174744

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0811.3521
 http://arxiv.org/abs/0811.3521

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arXiv