Des codes pour engendrer des langages de mots infinis

Vinh Duc Tran 1
1 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : This thesis deals with the languages of infinite words which are the ω-powers of a language of finite words. In particular, we focus on the open question : given a language L, does there exist an ω-code C such that C^ω = L^ω ? It is quite similar to the question deciding whether a submonoid of a free monoid is generated by a code. First, we study the set of relations satisfied by language L, i.e. the double factorizations of a word in L^∗ ∪ L^ω. We establish a necessary condition for that L^ω has a code or an ω-code generator. Next, we define the new class of languages where the set of relations is as simple as possible after codes : one-relation languages. For this class of languages, we characterize the languages L such that there exists a code or an ω-code C such that L^ω = C^ω, and we show that C is never a finite language. Finally, a characterization of codes concerning infinite words leads us to define reduced languages. We consider the properties of these languages as generators of languages of infinite words.
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Vinh Duc Tran. Des codes pour engendrer des langages de mots infinis. Théorie et langage formel [cs.FL]. Université Nice Sophia Antipolis, 2011. Français. ⟨tel-01288662⟩

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