Generating functions of timed languages

Authors:
Eugene Asarin;Nicolas Basset;Aldric Degorre;Dominique Perrin
Affiliations:
LIAFA, University Paris Diderot and CNRS, France;LIGM, University Paris-Est Marne-la-Vallée and CNRS, France;LIAFA, University Paris Diderot and CNRS, France;LIGM, University Paris-Est Marne-la-Vallée and CNRS, France
Venue:
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Year:
2012

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Abstract

In order to study precisely the growth of timed languages, we associate to such a language a generating function. These functions (tightly related to volume and entropy of timed languages) satisfy compositionality properties and, for deterministic timed regular languages, can be characterized by integral equations. We provide procedures for closed-form computation of generating functions for some classes of timed automata and regular expressions.