Proving ATL* Properties of Infinite-State Systems

Abstract

AbstractAlternating temporal logic (atl*) was introduced to prove properties of multi-agent systems in which the agents have different objectives and may collaborate to achieve them. Examples include (distributed) controlled systems, security protocols, and contract-signing protocols. Proving atl* properties over finite-state systems was shown decidable by Alur et al., and a model checker for the sublanguage atl implemented in mocha.In this paper we present a sound and complete proof system for proving alt* properties over infinite-state systems. The proof system reduces proofs of alt* properties over systems to first-order verification conditions in the underlying assertion language. The verification conditions make use of predicate transformers that depend on the system structure, so that proofs over systems with a simpler structure, e.g., turn-based systems, directly result in simpler verification conditions. We illustrate the use of the proof system on a small example.KeywordsRanking FunctionProof SystemProof RuleFairness ConditionPredicate TransformerThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.