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Theses
Des codes pour engendrer des langages de mots infinis
Des codes pour engendrer des langages de mots infinis
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.
Cited literature [35 references]
https://tel.archives-ouvertes.fr/tel-01288662
Contributor : Sandrine Julia <>
Submitted on : Tuesday, March 15, 2016 - 4:55:35 PM
Last modification on : Wednesday, October 14, 2020 - 4:23:04 AM
Long-term archiving on: : Thursday, June 16, 2016 - 10:43:26 AM
Contributor : Sandrine Julia <>
Submitted on : Tuesday, March 15, 2016 - 4:55:35 PM
Last modification on : Wednesday, October 14, 2020 - 4:23:04 AM
Long-term archiving on: : Thursday, June 16, 2016 - 10:43:26 AM