In this paper, we study algorithmic problems for automaton semigroups and automaton
groups related to freeness and finiteness. In the course of this study, we also exhibit some …

In this paper, we study the word problem for automaton semigroups and automaton groups
from a complexity point of view. As an intermediate concept between automaton semigroups …

The class of automaton groups is a rich source of the simplest examples of infinite Burnside
groups. However, all such examples have been constructed as groups generated by non …

This collaborative volume aims at presenting and develo** recent trends at the interface
between the study of sequences, groups, and number theory, as the title may suggest. It is …

We prove that the boundary dynamics of the (semi) group generated by the enriched dual
transducer characterizes the algebraic property of being free for an automaton group. We …

We show that an automaton group or semigroup is infinite if and only if it admits an ω-word
(ie a right-infinite word) with an infinite orbit, which solves an open problem communicated …

This paper deals with graph automaton groups associated with trees and some
generalizations. We start by showing some algebraic properties of tree automaton groups …

The simplest example of an infinite Burnside group arises in the class of automaton groups.
However there is no known example of such a group generated by a reversible Mealy …

We study automaton groups without singular points, that is, points in the boundary for which
the map that associates to each point its stabilizer, is not continuous. This is motivated by the …

We study the dynamics of the action of an automaton group on the set of infinite words, and
more precisely the discontinuous points of the map which associates to a point its set of …