Local Model Checking in a Logic for True Concurrency

Abstract

We provide a model-checking technique for a logic for true concurrency, whose formulae predicate about events in computations and their causal dependencies. The logic, that represents the logical counterpart of history-preserving bisimilarity, is naturally interpreted over event structures. It includes minimal and maximal fixpoint operators and thus it can express properties of infinite computations. Global algorithms are not convenient in this setting, since the event structure associated with a system is typically infinite (even if the system is finite state), a fact that makes also the decidability of model-checking non-trivial. Focusing on the alternation free fragment of the logic, along the lines of some classical work for the modal mu-calculus, we propose a local model-checking algorithm. The algorithm is given in the form of a tableau system, for which, over a class of event structures satisfying a suitable regularity condition, we prove termination, soundness and completeness.