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Model completeness, uniform interpolants and superposition calculus. (With applications to verification of data-aware processes). (English) Zbl 07433024

Summary: Uniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as “covers”) in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by S. Gulwani and M. Musuvathi [Lect. Notes Comput. Sci. 4960, 193–207 (2008; Zbl 1133.68318)], and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution.

MSC:

68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)

Citations:

Zbl 1133.68318

Software:

Mcmt; VERIFAS; Cubicle
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