Abstract
Craig interpolation has emerged as an effective means of generating candidate program invariants. We present interpolation procedures for the theories of Presburger arithmetic combined with (i) uninterpreted predicates (QPA+UP), (ii) uninterpreted functions (QPA+UF) and (iii) extensional arrays (QPA+AR). We prove that none of these combinations can be effectively interpolated without the use of quantifiers, even if the input formulae are quantifier-free. We go on to identify fragments of QPA+UP and QPA+UF with restricted forms of guarded quantification that are closed under interpolation. Formulae in these fragments can easily be mapped to quantifier-free expressions with integer division. For QPA+AR, we formulate a sound interpolation procedure that potentially produces interpolants with unrestricted quantifiers.
This research is supported by the EPSRC project EP/G026254/1, by the EU FP7 STREP MOGENTES, and by the EU ARTEMIS CESAR project.
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Brillout, A., Kroening, D., Rümmer, P., Wahl, T. (2011). Beyond Quantifier-Free Interpolation in Extensions of Presburger Arithmetic. In: Jhala, R., Schmidt, D. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2011. Lecture Notes in Computer Science, vol 6538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18275-4_8
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DOI: https://doi.org/10.1007/978-3-642-18275-4_8
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