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External power of a deterministic automaton, application to the zeta-function of a sofic system. (Puissance extérieure d’un automate déterministe, application au calcul de la fonction zêta d’un système sofique.) (French) Zbl 0843.58035

Summary: We define a construction with finite deterministic automata, called external power. These constructions are used to give a combinatorial and simple proof of the rationality of the generalized zeta function of a sofic system.

MSC:

37E99 Low-dimensional dynamical systems
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
68Q70 Algebraic theory of languages and automata
68Q45 Formal languages and automata
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References:

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