Forbidden Words in Symbolic Dynamics

Forbidden Words in Symbolic Dynamics

We introduce an equivalence relation between functions from to . 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 sof...

Minimal Forbidden Words and Symbolic Dynamics Classiication: Automata and Formal Languages

We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system deened by L.

Combinatorics, Words and Symbolic Dynamics

Automata and Forbidden Words

Let L(M) be the (factorial) language avoiding a given anti-factorial language M. We design an automaton accepting L(M) and built from the language M. The construction is eeective if M is nite. If M is the set of minimal forbidden words of a single word v, the automaton turns out to be the factor automaton of v (the minimal automaton accepting the set of factors of v). We also give an algorithm ...

Words and forbidden factors

Given a *nite or in*nite word v, we consider the set M (v) of minimal forbidden factors of v. We show that the set M (v) is of fundamental importance in determining the structure of the word v. In the case of a *nite word w we consider two parameters that are related to the size of M (w): the *rst counts the minimal forbidden factors of w and the second gives the length of the longest minimal f...