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On the Complexity of the Word Problem of Automaton Semigroups and Automaton Groups | | Daniele D'Angeli
; Emanuele Rodaro
; Jan Philipp Wächter
; | | Date: |
29 Nov 2016 | | Abstract: | In this paper, we study the word problem of 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 whose 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. | | Source: | arXiv, 1611.9541 | | Services: | Forum | Review | PDF | Favorites | |
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