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An interpolating sequent calculus for quantifier-free Presburger arithmetic
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computer Systems. (Embedded Systems)
2011 (English)In: Journal of automated reasoning, ISSN 0168-7433, E-ISSN 1573-0670, Vol. 47, no 4, 341-367 p.Article in journal (Refereed) Published
Abstract [en]

Craig interpolation has become a versatile tool in formal verification, used for instance to generate program assertions that serve as candidates for loop invariants. In this paper, we consider Craig interpolation for quantifier-free Presburger arithmetic (QFPA). Until recently, quantifier elimination was the only available interpolation method for this theory, which is, however, known to be potentially costly and inflexible. We introduce an interpolation approach based on a sequent calculus for QFPA that determines interpolants by annotating the steps of an unsatisfiability proof with partial interpolants. We prove our calculus to be sound and complete. We have extended the Princess theorem prover to generate interpolating proofs, and applied it to a large number of publicly available Presburger arithmetic benchmarks. The results document the robustness and efficiency of our interpolation procedure. Finally, we compare the procedure against alternative interpolation methods, both for QFPA and linear rational arithmetic.

Place, publisher, year, edition, pages
2011. Vol. 47, no 4, 341-367 p.
National Category
Computer Science
URN: urn:nbn:se:uu:diva-165089DOI: 10.1007/s10817-011-9237-yISI: 000297732500002OAI: oai:DiVA.org:uu-165089DiVA: diva2:471734
Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2015-07-24Bibliographically approved

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