In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSPACE-complete word problem. We also show that there is an automaton group for which the word problem with a single rational constraint is PSPACE-complete. Additionally, we provide simpler constructions for the uniform word problems of these classes. For the uniform word problem for automaton groups (without rational constraints), we show NL-hardness. Finally, we investigate a question asked by Cain about a better upper bound for the length of a word on which two distinct elements of an automaton semigroup must act differently. A detailed listing of the contributions of this paper can be found at the end of this paper.
|Titolo:||On the complexity of the word problem for automaton semigroups and automaton groups|
|Data di pubblicazione:||2017|
|Appare nelle tipologie:||01.1 Articolo in Rivista|
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|PSPACE word proble automaton semigroups.pdf||Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)||Accesso riservato|