Abstract
The problem of computing Craig interpolants in SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of interest –including that of equality and uninterpreted functions (\(\mathcal{EUF}\)), linear arithmetic over the rationals (\(\mathcal{LA}(\mathbb{Q})\)), and some fragments of linear arithmetic over the integers (\(\mathcal{LA}(\mathbb{Z})\))– and they are successfully used within model checking tools.
In this paper we address the problem of computing interpolants in the theory of Unit-Two-Variable-Per-Inequality (\(\mathcal{UTVPI}\)). This theory is a very useful fragment of \(\mathcal{LA}(\mathbb{Z})\), since it is expressive enough to encode many hardware and software verification queries while still admitting a polynomial time decision procedure. We present an efficient graph-based algorithm for interpolant generation in \(\mathcal{UTVPI}\), which exploits the power of modern SMT techniques. We have implemented our new algorithm within the MathSAT SMT solver. Our experimental evaluation demonstrates both the efficiency and the usefulness of the new algorithm.
The first author is partly supported by the European Commission under project FP7-2007-IST-1-217069 COCONUT. The second and third authors are partly supported by SRC under GRC Custom Research Project 2009-TJ-1880 WOLFLING, and by MIUR under PRIN project 20079E5KM8_002.
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Cimatti, A., Griggio, A., Sebastiani, R. (2009). Interpolant Generation for UTVPI. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_15
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DOI: https://doi.org/10.1007/978-3-642-02959-2_15
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