Spectral Gap in Timed Automata

Eugene Asarin (1) , Aldric Degorre (1) , Nicolas Basset (1, 2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domaines: Théorie et langage formel [cs.FL]

Eugene Asarin, Aldric Degorre, Nicolas Basset. Spectral Gap in Timed Automata. FORMATS 2013, Aug 2013, Argentina. pp.16-30, ⟨10.1007/978-3-642-40229-6_2⟩. ⟨hal-00862273⟩