36 citations · 99 across the 12 of their papers we have counts for
15 papers
A new hierarchy for automaton semigroups
Laurent Bartholdi, Thibault Godin, Ines Klimann +1
We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy…
Automatic semigroups vs automaton semigroups
Matthieu Picantin
We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup,namely the semigroup generated…
Boundary action of automaton groups without singular points and Wang tilings
D. D'Angeli, Th. Godin, I. Klimann +2
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 motiva…
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…
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…
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.…