Combined Covers and Beth Definability
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In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exploited it to handle infinite-state model checking problems. Motivated by applications to the verification of data-aware processes, we proved in a previous paper that covers are strictly related to model completions, a well-known topic in model theory. In this paper we investigate cover transfer to theory combinations in the disjoint signatures case. We prove that for convex theories, cover algorithms can be transferred to theory combinations under the same hypothesis (equality interpolation property aka strong amalgamation property) needed to transfer quantifier-free interpolation. In the non-convex case, we show by a counterexample that cover may not exist in the combined theories. However, we exhibit a cover transfer algorithm operating also in the non-convex case for special kinds of theory combinations; these combinations (called `tame combinations') concern multi-sorted theories arising in many model-checking applications (in particular, in model-checking applications oriented to data-aware verification).
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