Quasi-identities of finite semigroups and symbolic dynamics

Quasi-identities of Finite Semigroups and Symbolic Dynamics

An algebra is inherently non-nitely (Q-)based if it is not a member of any locally nite (quasi-)variety, whose (quasi-)identities are nitely based. We prove that no nite semigroup is inherently non-nitely Q-based. This is in marked contrast to the case of varieties, where there are many inherently non-nitely based nite semigroups which have all been described by the second author.

Dynamics of Finite Semigroups

Symbolic Dynamics and Finite

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...

Computational Complexity of Checking Identities in 0-simple Semigroups and Matrix Semigroups over Finite Fields

In this paper we analyze the so called word-problem for (finite) combinatorial 0-simple semigroups and matrix semigroups from the viewpoint of computational complexity.