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 soc 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 \dierent slope" are not conjugate. Classication: Symbolic Dynamics, Combinatoric on words, Automata and Formal Languages. 1 Introduction In this paper we present a new topological invariant for Symbolic Dynamics. The techniques we use and some complementary results are from Combinatorics on words and from the theory of Automata and Formal Languages. Indeed there...

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