A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group
Document Type
Article
Publication Date
2018
Keywords
Burnside groups, reversible Mealy automata, automaton groups
Digital Object Identifier (DOI)
https://doi.org/10.1142/S0129054118400087
Abstract
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.
Was this content written or created while at USF?
Yes
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.
https://digitalcommons.usf.edu/mth_facpub/135
