The control part of many concurrent and distributed programs reduces to a set Π = {p1, . . . , pn} of symmetric processes containing mainly assignments and tests on Boolean variables. However, the assignments, the guards and the program invariants can be Π-quantified, so the corresponding verification conditions also involve Π-quantifications. We propose a systematic procedure allowing the elimination of such quantifications for a large class of program invariants. At the core of this procedure is a variant of the Herbrand Theorem for many-sorted first-order logic with equality.
Abstract. The algorithm for mutual exclusion proposed by B. Szymanski is an interesting challenge for verification methods and tools. Several full proofs have been described in the literature, but they seem to require lengthy interactive sessions with powerful theorem provers. As far as this algorithm makes use of only the most elementary facts of arithmetics, we conjectured that a simple, non-interactive proof should exist; this paper gives such a proof, describes its development and how an elementaxy tool has been used to complete the verification.
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