Thèse soutenue

Méthodes algébriques pour la théorie des automates
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Auteur / Autrice : Luc Dartois
Direction : Olivier CartonJean-Éric Pin
Type : Thèse de doctorat
Discipline(s) : Informatique
Date : Soutenance en 2014
Etablissement(s) : Paris 7

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Résumé

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In this thesis, we extend the links between the different models of representation of rational languages that are automata, logic and monoids through two extensions of these theories. The first contribution concerns the two-way transducers, an extension of automata defining transformations of words. We first propound the construction of the transitions monoid of two-way machines. This allows us to define the notion of aperiodic two-way transducers. We finally prove that this class is stable by composition. The second contribution concerns logic on finite words. The definability problem of a fragment of logic consists in deciding whether a given regular language can be defined by a formula of the said fragment. We study the decidability of this question when the signature of a fragment is enriched, in our case by predicates handling the modular information of the positions. Thanks to algebraic methods, we were able to gather transfer results to enriched fragments, unifying known results as well as obtaining new ones.