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Three complexity functions

Published online by Cambridge University Press:  23 November 2011

Sébastien Ferenczi  and
Pascal Hubert
Sébastien Ferenczi
Affiliation:
Institut de Mathématiques de Luminy, CNRS UMR 6206, Case 907, 163 av. de Luminy, 13288 Marseille Cedex 9, France. ferenczi@iml.univ-mrs.fr Fédération de Recherche des Unités de Mathématiques de Marseille, CNRS FR, 2291, France
Pascal Hubert
Affiliation:
Fédération de Recherche des Unités de Mathématiques de Marseille, CNRS FR, 2291, France Laboratoire d’Analyse, Topologie et Probabilités, CNRS UMR 6632, Case A, Faculté de Saint Jérôme, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France; hubert@cmi.univ-mrs.fr
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Abstract

For an extensive range of infinite words, and the associated symbolic dynamical systems, we compute, together with the usual language complexity function counting the finite words, the minimal and maximal complexity functions we get by replacing finite words by finite patterns, or words with holes.

Keywords

Infinite wordssymbolic dynamical systemscomplexity

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