A Characterization of Those Automata That Structurally Generate Finite Groups

@article{Klimann2014ACO,
  title={A Characterization of Those Automata That Structurally Generate Finite Groups},
  author={Ines Klimann and Matthieu Picantin},
  journal={ArXiv},
  year={2014},
  volume={abs/1310.7137}
}
  • Ines Klimann, Matthieu Picantin
  • Published in LATIN 2014
  • Computer Science, Mathematics
  • ArXiv
  • Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper. 

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