Some structural properties of the free profinite aperiodic semigroup

Jorge Almeida (1) , José-Carlos Costa (2) , Marc Zeitoun (3)

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

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.

Domaines: Théorie et langage formel [cs.FL]

Jorge Almeida, José-Carlos Costa, Marc Zeitoun. Some structural properties of the free profinite aperiodic semigroup. Automatha Plenary Conference, Jun 2009, Belgium. ⟨hal-00948998⟩