Abstract

We define a general framework for the extension of temporal logics with constraints induced by a concrete domain, made of an interpretation domain and a set of relations. The extensions we consider allow to compare values of the variables at different states of an execution. We establish decidability and complexity results for several model-checking problems involving several instances of such extensions. We mainly use automata-based techniques that combine some usual constructions for temporal logics with finite abstraction methods for infinite datas. For instance, we consider several fragments of (linear and branching-time) temporal logics extended with constraints on counters induced by Presburger arithmetic.

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