Profinite semigroups

Decidability and Tameness in the Theory of Finite Semigroups

Profinite semigroups and applications∗

Profinite semigroups may be described shortly as projective limits of finite semigroups. They come about naturally by studying pseudovarieties of finite semigroups which in turn serve as a classifying tool for rational languages. Of particular relevance are relatively free profinite semigroups which for pseudovarieties play the role of free algebras in the theory of varieties. Combinatorial pro...

Subword Complexity of Profinite Words and Subgroups of Free Profinite Semigroups

We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated implicit operators, subword complexity and the associated entropy.

Symbolic Dynamics in Free Profinite Semigroups

This is a survey and announcement of recent results on the structure of free profinite semigroups using techniques and results from symbolic dynamics. The intimate connection between uniformly recurrent infinite words and J -maximal regular J -classes is explored to compute the maximal subgroups of the J -classes associated with Arnoux-Rauzy infinite words, which turn out to be free profinite g...

Some structural properties of the free profinite aperiodic semigroup

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 semigroups. In this paper, we present new results obtained for the class of all finite aperiodic (that is, group-free) semigroups. Given a finite alphabet X, we focus on the following problems: (...