M . Baclet Logical Characterization of Aperiodic Data Languages

Data languages are an extension of timed languages, as defined by R. Alur and D. L. Dill, proposed by P. Bouyer, A. Petit and D. Thérien to provide a suitable theoretical framework, comparable to the formal languages theory. A class of data languages, naturally called recognizable data languages, can be defined in an equivalent way by automata, finite monoids and logic formulas. The aim of this paper is to study the subclass of recognizable data languages which are defined by aperiodic monoids. Note that the corresponding class for formal languages plays a central role in the verification of untimed systems. For instance, a recognizable formal language is defined by a first order logic formula (or by a linear temporal logic formula) if and only if it is recognized by an aperiodic monoid. We propose extensions of this deep result to data languages framework.