Sur la complexité de mots infinis engendrés par des $q$-automates dénombrables

Le Gonidec, Marion

Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2463-2491.

On étudie, dans cet article, les propriétés combinatoires de mots engendrés à l’aide de $q$-automates déterministes dénombrables de degré borné, ou de manière équivalente, engendrés par des substitutions de longueur constante uniformément bornées sur un alphabet dénombrable. En particulier, on montre que la complexité de tels mots est au plus polynomiale et que, sur plusieurs exemples, elle est au plus de l’ordre de grandeur de $n{(logn)}^p$.

This article deals with combinatorial properties of infinite words generated by countable and deterministic $q$-automata of bounded degree. Those words can also be viewed as projections of fixed point of some substitutions of constant length on countable alphabet. We show that complexity function of such words is at most polynomial and, on some examples, the order of growth of this function is at most $n{(logn)}^p$.

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