Minimal forbidden words and factor automata

Abstract : Let L(M) be the (factorial) language avoiding a given antifactorial language M. We design an automaton accepting L(M) and built from the language M. The construction is eff ective if M is finite. 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 that builds the trie of M from the factor automaton of a single word. It yields a non-trivial upper bound on the number of minimal forbidden words of a word.
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Maxime Crochemore, Filippo Mignosi, Antonio Restivo. Minimal forbidden words and factor automata. Mathematical Foundations of Computer Science (Brno, 1998), 1998, France. pp.665-673. ⟨hal-00619990⟩

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