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* Corresponding author 1 UNIVERSIDADE DO PORTO - Departamento de Matemática Pura, Faculdade de Ciências 2 CMAT - Centro de Matemática Minho 3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Abstract : Profinite semigroups provide powerful tools to understand properties of classes of regular languages. Until very recently however, little was known on the structure of -large- relatively free profinite semi- groups. In this paper, we present new results obtained for the class of all finite aperiodic that is, group-free semigroups. Given a finite al- phabet X, we focus on the following problems: 1 the word problem for ω-terms on X evaluated on the free pro-aperiodic semigroup, and 2 the computation of closures of regular languages in the ω-subsemigroup of the free pro-aperiodic semigroup generated by X.





Author: Jorge Almeida - José-Carlos Costa - Marc Zeitoun -

Source: https://hal.archives-ouvertes.fr/



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