Spectral Gap in Timed Automata

  • Eugene Asarin
  • Nicolas Basset
  • Aldric Degorre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8053)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Eugene Asarin
    • 1
  • Nicolas Basset
    • 1
    • 2
  • Aldric Degorre
    • 1
  1. 1.LIAFAUniversity Paris Diderot and CNRSFrance
  2. 2.LIGMUniversity Paris-Est Marne-la-Vallée and CNRSFrance

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