On the orbits of automaton semigroups and groups

• Date: 2022
• Main Authors: D'Angeli, D., Francoeur, D., Rodaro, E., Wächter, J. Ph.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: automaton groups; automaton semigroups; orbits; Schreier graphs; orbital graphs; reversible; 20E99; 20F10; 20M30; 20M35; 68Q70
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1692
• Journal Title: Algebra and Discrete Mathematics

We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses.First, we show that a more general version of the finiteness problem for automaton groups is undecidable. This problem is equivale...