Regular Article: Forbidden Words in Symbolic Dynamics

Authors:
M.-P Béal;F Mignosi;A Restivo;M Sciortino
Affiliations:
Institut Gaspard Monge, Université de Marne la Vallée, 5 Bd Descartes, Champs-sur-Marne, F-77454, Marne la Vallée, Francef1beal@univ-mlv.frf1;Dipartimento di Matematica ed Applicazioni, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy;Dipartimento di Matematica ed Applicazioni, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy;Dipartimento di Matematica ed Applicazioni, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy
Venue:
Advances in Applied Mathematics
Year:
2000

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Abstract

We introduce an equivalence relation~between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the~-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of sofic systems, we prove that the~-equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having ''different slope'' are not conjugate.