A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group
Burnside groups, reversible Mealy automata, automaton groups
Digital Object Identifier (DOI)
The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, all such examples have been constructed as groups generated by non-reversible automata. Moreover, it was recently shown that 2-state reversible Mealy automata cannot generate infinite Burnside groups. Here we extend this result to connected 3-state reversible Mealy automata, using new original techniques. The results rely on a fine analysis of associated orbit trees and a new characterization of the existence of elements of infinite order.
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Citation / Publisher Attribution
International Journal of Foundations of Computer Science, v. 29, issue 2, p. 297-314
Scholar Commons Citation
Klimann, Ines; Picantin, Matthieu; and Savchuk, Dmytro, "A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group" (2018). Mathematics and Statistics Faculty Publications. 135.