Timed symbolic dynamics

Dynamique symbolique temporisée

Nicolas Basset (1)

1 Department of Computer Science [Oxford]

We introduce a theory of timed symbolic dynamics unifying results from timed automata theory and symbolic dynamics. The timed sofic shift spaces we define are a way of seeing timed regular languages as shift spaces on general alphabets (in classical symbolic dynamics, sofic shift spaces correspond to regular languages). We show that morphisms of shift space on general alphabet can be approximated by sliding block codes resulting in a generalised version of the so-called Curtis-Hedlund-Lyndon Theorem. We provide a new measure for timed languages by characterising the Gromov-Lindenstrauss-Weiss metric mean dimension for timed shift spaces and illustrate it on several examples. We revisit recent results on volumetry of timed languages of Asarin, Degorre and us in terms of timed symbolic dynamics. In particular we explain the discretisation of timed shift spaces and their entropy.

Domaines: Informatique et langage [cs.CL]; Systèmes dynamiques [math.DS]

Nicolas Basset. Timed symbolic dynamics. [Research Report] University of Oxford. 2015. ⟨hal-01094105v2⟩