Corpus ID: 67855910

Orbits of Automaton Semigroups and Groups

@article{DAngeli2019OrbitsOA,
  title={Orbits of Automaton Semigroups and Groups},
  author={D. D'Angeli and Dominik Francoeur and E. Rodaro and Jan Philipp W{\"a}chter},
  journal={ArXiv},
  year={2019},
  volume={abs/2007.10273}
}
We study the orbits of right infinite or $\omega$-words under the action of semigroups and groups generated by automata. We see that an automaton group or semigroup is infinite if and only if it admits an $\omega$-word with an infinite orbit, which solves an open problem communicated to us by Ievgen V. Bondarenko. In fact, we prove a generalization of this result, which can be applied to show that finitely generated subgroups and subsemigroups as well as principal left ideals of automaton… Expand
Orbit Expandability of Automaton Semigroups and Groups

References

SHOWING 1-10 OF 34 REFERENCES
Automaton semigroup constructions
Orbit Expandability of Automaton Semigroups and Groups
Automaton semigroups: New constructions results and examples of non-automaton semigroups
On the structure theory of partial automaton semigroups
Automaton semigroups and groups: On the undecidability of problems related to freeness and finiteness
On the Complexity of the Word Problem of Automaton Semigroups and Automaton Groups
Freeness of automata groups vs boundary dynamics
Automaton semigroups
  • Alan J. Cain
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 2009
...
1
2
3
4
...