Automatic Verification of Probabilistic Free Choice

We study automatic methods for establishing P-validity (validity with probability 1) of simple temporal properties over finite-state probabilistic systems. The proposed approach replaces P-validity with validity over a non-probabilistic version of the system, in which probabilistic choices are replaced by non-deterministic choices constrained by compassion (strong fairness) requirements. "Simple" properties are temporal properties whose only temporal operators are l (eventually) and its dual ? (always). In general, the appropriate compassion requirements are "global," since they involve global states of the system. Yet, in many cases they can be transformed into "local" requirements, which enables their verification by model checkers. We demonstrate our methodology of translating the problem of P-validity into that of verification of a system with local compassion requirement on the "courteous philosophers" algorithm of [LR81], a parameterized probabilistic system that is notoriously difficult to verify, and outline a verification of the algorithm that was obtained by the tlv model checker.

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