Abstract
Craig interpolation has become a key ingredient in many symbolic model checkers, serving as an approximative replacement for expensive quantifier elimination. In this paper, we focus on an interpolating decision procedure for the full quantifier-free fragment of Presburger Arithmetic, i.e., linear arithmetic over the integers, a theory which is a good fit for the analysis of software systems. In contrast to earlier procedures based on quantifier elimination and the Omega test, our approach uses integer linear programming techniques: relaxation of interpolation problems to the rationals, and a complete branch-and-bound rule tailored to efficient interpolation. Equations are handled via a dedicated polynomial-time sub-procedure. We have fully implemented our procedure on top of the SMT-solver OpenSMT and present an extensive experimental evaluation.
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Kroening, D., Leroux, J., Rümmer, P. (2010). Interpolating Quantifier-Free Presburger Arithmetic . In: Fermüller, C.G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science, vol 6397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16242-8_35
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DOI: https://doi.org/10.1007/978-3-642-16242-8_35
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