Two Size Measures for Timed Languages

Abstract : Quantitative properties of timed regular languages, such as information content (growth rate, entropy) are explored. The approach suggested by the same authors is extended to languages of timed automata with punctual (equalities) and non-punctual (non-equalities) transition guards. Two size measures for such languages are identified: mean dimension and volumetric entropy. The former is the linear growth rate of the dimension of the language; it is characterized as the spectral radius of a max-plus matrix associated to the automaton. The latter is the exponential growth rate of the volume of the language; it is characterized as the logarithm of the spectral radius of a matrix integral operator on some Banach space associated to the automaton. Relation of the two size measures to classical information-theoretic concepts is explored.
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Pré-publication, Document de travail
A short version (without appendix) of this paper will appear in proceedings of FSTTCS'2010 (in LI.. 2010
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Eugene Asarin, Aldric Degorre. Two Size Measures for Timed Languages. A short version (without appendix) of this paper will appear in proceedings of FSTTCS'2010 (in LI.. 2010. <hal-00527852>

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