Spectral gap in timed automata

Authors:
Eugene Asarin;Nicolas Basset;Aldric Degorre
Affiliations:
LIAFA, University Paris Diderot and CNRS, France;LIAFA, University Paris Diderot and CNRS, France,LIGM, University Paris-Est Marne-la-Vallée and CNRS, France;LIAFA, University Paris Diderot and CNRS, France
Venue:
FORMATS'13 Proceedings of the 11th international conference on Formal Modeling and Analysis of Timed Systems
Year:
2013

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Abstract

Various problems about probabilistic and non-probabilistic timed automata (computing probability density, language volume or entropy) can be naturally phrased as iteration of linear operators in Banach spaces. Convergence of such iterations is guaranteed whenever the operator's spectrum has a gap. In this article, for operators used in entropy computation, we use the theory of positive operators to establish the existence of such a gap. This allows to devise simple numeric algorithms for computing the entropy and prove their exponential convergence.