Thibault Godin

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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 with the same input and output alphabet. The torsion problem is undecidable for automaton semigroups in general, but is known to be solvable within the well-studied class of(More)
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 problem of finding examples of infinite bireversible automaton groups with all trivial stabilizers in the boundary, raised by Grigorchuk and Savchuk. We show that, in(More)
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 automaton. It has been proved that, for a connected automaton of size at most 3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite. In this(More)
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