Abstract
We have recently defined size measures for timed languages: volume for languages with words having a fixed finite number of events, and entropy (growth rate) as asymptotic measure for an unbounded number of events. These measures can be used for quantitative comparison of languages, and the entropy can be viewed as the information contents of a timed language. For languages accepted by deterministic timed automata, using methods of functional analysis, we characterize the entropy as the logarithm of the leading eigenvalue (spectral radius) of a positive integral operator. We devise two procedures to compute the entropy: a symbolic one for so-called “\(1\, \frac{1}{2}\)-clock” automata, using differential equations; and a numerical one based on iterations of an integral operator.
Support from French ANR project AMAES is gratefully acknowledged.
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Asarin, E., Degorre, A. (2009). Volume and Entropy of Regular Timed Languages: Analytic Approach. In: Ouaknine, J., Vaandrager, F.W. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2009. Lecture Notes in Computer Science, vol 5813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04368-0_4
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DOI: https://doi.org/10.1007/978-3-642-04368-0_4
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