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 …

Full article: The Lamplighter Group ℤ3≀ℤ Generated by a Bireversible Automaton Skip to Main
Content Taylor and Francis Online homepage Taylor and Francis Online homepage Log in …

We prove that semigroups generated by reversible two-state Mealy automata have
remarkable growth properties: they are either finite or free. We give an effective procedure to …

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 give a geometric approach to groups defined by automata via the notion of enriched
dual of an inverse transducer. Using this geometric correspondence we first provide some …

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 …

We address the problem of finding examples of non-bireversible transducers defining free
groups, we show examples of transducers with sink accessible from every state which …

Schreier graphs of an extended version of the binary adding machine Page 1 Schreier
graphs of an extended version of the binary adding machine Daniele D’Angeli ∗ Institut für …