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An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic

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Abstract

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.

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Authors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Angelo Brillout

  2. Computer Science Department, Oxford University, Oxford, UK

    Daniel Kroening & Thomas Wahl

  3. Department of Information Technology, Uppsala University, Uppsala, Sweden

    Philipp Rümmer

Authors
  1. Angelo Brillout
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  2. Daniel Kroening
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  3. Philipp Rümmer
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  4. Thomas Wahl
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Corresponding author

Correspondence to Philipp Rümmer.

Additional information

This paper is an extended version of a publication that appeared at IJCAR [3].

Supported by the Engineering and Physical Sciences Research Council (EPSRC) under grant no. EP/G026254/1, by the EU FP7 STREP MOGENTES, by the EU FP7 STREP PINCETTE, and by the EU ARTEMIS project CESAR.

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Brillout, A., Kroening, D., Rümmer, P. et al. An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic. J Autom Reasoning 47, 341–367 (2011). https://doi.org/10.1007/s10817-011-9237-y

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  • DOI: https://doi.org/10.1007/s10817-011-9237-y

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