automaton semigroups
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Author(s):  
Laurent Bartholdi ◽  
Thibault Godin ◽  
Ines Klimann ◽  
Camille Noûs ◽  
Matthieu Picantin

We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy extends that given by Sidki for automaton groups, and also gives new insights into the latter. Its exponential part coincides with a notion of entropy for some associated automata. We prove that the Order Problem is decidable whenever the state-activity is bounded. The Order Problem remains open for the next level of this hierarchy, that is, when the state-activity is linear. Gillibert showed that it is undecidable in the whole family. We extend the aforementioned hierarchy via a semi-norm making it more coarse but somehow more robust and we prove that the Order Problem is still decidable for the first two levels of this alternative hierarchy.


2020 ◽  
Vol 101 (1) ◽  
pp. 51-76
Author(s):  
Daniele D’Angeli ◽  
Emanuele Rodaro ◽  
Jan Philipp Wächter

2020 ◽  
Vol 553 ◽  
pp. 119-137 ◽  
Author(s):  
Daniele D'Angeli ◽  
Dominik Francoeur ◽  
Emanuele Rodaro ◽  
Jan Philipp Wächter
Keyword(s):  

2020 ◽  
Vol 237 (1) ◽  
pp. 15-52 ◽  
Author(s):  
Daniele D’Angeli ◽  
Emanuele Rodaro ◽  
Jan Philipp Wächter
Keyword(s):  

2020 ◽  
Vol 809 ◽  
pp. 418-429 ◽  
Author(s):  
Daniele D'Angeli ◽  
Emanuele Rodaro ◽  
Jan Philipp Wächter
Keyword(s):  

Author(s):  
Laurent Bartholdi ◽  
Thibault Godin ◽  
Ines Klimann ◽  
Matthieu Picantin
Keyword(s):  

2017 ◽  
Vol 90 ◽  
pp. 160-187 ◽  
Author(s):  
Daniele D'Angeli ◽  
Emanuele Rodaro ◽  
Jan Philipp Wächter

2014 ◽  
Vol 58 (4) ◽  
pp. 664-680 ◽  
Author(s):  
Ines Klimann

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