… freeness problem for automaton (semi)groups. Inspired by links between the freeness of an
automaton group and the dynamics on periodic points in the boundary of the dual automaton …

… freeness of the groups generated by an invertible transducer in term of the dynamics on the
boundary of group … for the group (semigroup) generated by the dual automaton. Subsequently…

… connections between group theory and automata theory. We … connections; we see automata
used to encode complexity, to … free group on X; if |X| = k, then we say that F is the free group …

… We show that the freeness problems for automaton semigroups and for automaton monoids
are … In fact, there is a large body of work on the presentation of free groups (and semigroups) …

… by a valence automaton over a torsion group has a semilinear Parikh image. On the one …
every monoid M, the languages accepted by valence automata over M either (1) coincide with …

… whether the freeness problem for automaton semigroups is … If the semigroup S acts on the
left on some monoid M, we … product, we still have a connection concerning their freeness. …

… general results on profinite topologies on groups. For a general reference on the theory of
groups, the … But there is much more to be gained from the freeness of F(A): we now turn to the …

… freeness problems over various semigroups: … automaton over X is also an automaton over
any superset of X. In particular, for any alphabet Σ, an automaton over Σ is also an automaton …

… and was further extended to group actions on lR-trees and on more general A-trees. In …
group actions on A-trees, we look at the properties of n-freeness, local freeness and para-freeness…

… Once the bijection between subgroups and automata is established, we focus on some …
to be fundamental as it characterizes (group) freeness, and can consequently be taken as …