3 papers
math.GR2014
Orbit automata as a new tool to attack the order problem in automaton groups
Ines Klimann, Matthieu Picantin, Dmytro Savchuk
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group on the subtrees corresponding to the orbits of on levels of the tree. T…
cs.FL2014
On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata
Thibault Godin, Ines Klimann, Matthieu Picantin
This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers w…
cs.FL2014
A connected 3-state reversible Mealy automaton cannot generate an infinite Burnside group
Ines Klimann, Matthieu Picantin, Dmytro Savchuk
The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples.…