Topological Complexity of ω-Powers : Extended Abstract
نویسندگان
چکیده
1 Equipe Modèles de Calcul et Complexité Laboratoire de l’Informatique du Parallélisme CNRS et Ecole Normale Supérieure de Lyon 46, Allée d’Italie 69364 Lyon Cedex 07, France. [email protected] 2 Equipe d’Analyse Fonctionnelle Université Paris 6 4, place Jussieu, 75 252 Paris Cedex 05, France [email protected] and Université de Picardie, I.U.T. de l’Oise, site de Creil, 13, allée de la faı̈encerie, 60 107 Creil, France.
منابع مشابه
Topological Complexity of omega-Powers: Extended Abstract
The operation V → V ω is a fundamental operation over finitary languages leading to ω-languages. It produces ω-powers, i.e. ω-languages in the form V , where V is a finitary language. This operation appears in the characterization of the class REGω of ω-regular languages (respectively, of the class CFω of context free ω-languages) as the ω-Kleene closure of the family REG of regular finitary la...
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The operation V → V ω is a fundamental operation over finitary languages leading to ω-languages. Since the set Σ of infinite words over a finite alphabet Σ can be equipped with the usual Cantor topology, the question of the topological complexity of ω-powers of finitary languages naturally arises and has been posed by Niwinski [Niw90], Simonnet [Sim92] and Staiger [Sta97a]. It has been recently...
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The operation V → V ω is a fundamental operation over finitary languages leading to ω-languages. Since the set Σ of infinite words over a finite alphabet Σ can be equipped with the usual Cantor topology, the question of the topological complexity of ω-powers of finitary languages naturally arises and has been posed by Niwinski [Niw90], Simonnet [Sim92] and Staiger [Sta97a]. It has been recently...
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We prove that, for each countable ordinal ξ ≥ 1, there exist some Σ0ξ-complete ω-powers, and some Π0ξ-complete ω-powers, extending previous works on the topological complexity of ω-powers [Fin01, Fin03, Fin04, Lec01, Lec05, DF06]. We prove effective versions of these results; in particular, for each recursive ordinal ξ < ω 1 there exist some recursive sets A ⊆ 2 such that A∞ ∈ Π 0ξ \Σ 0 ξ (resp...
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