scholarly journals Bounded Automata Groups are co-ET0L

2019 ◽  
pp. 82-94
Author(s):  
Alex Bishop ◽  
Murray Elder
Keyword(s):  
Automata Groups

scholarly journals Spectral Analysis of Transition Operators, Automata Groups and Translation in BBS

2016 ◽  
Vol 350 (1) ◽  
pp. 205-229 ◽  
Author(s):  
Tsuyoshi Kato ◽  
Satoshi Tsujimoto ◽  
Andrzej Zuk
Keyword(s):  
Spectral Analysis ◽  
Automata Groups ◽  
Transition Operators

scholarly journals On amenability of automata groups

2010 ◽  
Vol 154 (3) ◽  
pp. 575-598 ◽  
Author(s):  
Laurent Bartholdi ◽  
Vadim A. Kaimanovich ◽  
Volodymyr V. Nekrashevych
Keyword(s):  
Automata Groups

scholarly journals On elementary amenable bounded automata groups

2021 ◽  
Vol 70 (6) ◽  
pp. 2479-2526
Author(s):  
Kate Juschenko ◽  
Benjamin Steinberg ◽  
Phillip Wesolek
Keyword(s):  
Automata Groups

scholarly journals Automata, groups, limit spaces, and tilings

2006 ◽  
Vol 305 (2) ◽  
pp. 629-663 ◽  
Author(s):  
Laurent Bartholdi ◽  
André G. Henriques ◽  
Volodymyr V. Nekrashevych
Keyword(s):  
Automata Groups

scholarly journals The word and order problems for self-similar and automata groups

2020 ◽  
Vol 14 (2) ◽  
pp. 705-728
Author(s):  
Laurent Bartholdi ◽  
Ivan Mitrofanov
Keyword(s):  
Automata Groups ◽  
Self Similar

ON A CLASS OF AUTOMATA GROUPS GENERALIZING LAMPLIGHTER GROUPS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1213-1234 ◽  
Author(s):  
P. V. SILVA ◽  
B. STEINBERG
Keyword(s):  
Parabolic Subgroups ◽  
Locally Finite ◽  
Cyclic Groups ◽  
Automata Groups ◽  
Lamplighter Group ◽  
Fractal Properties ◽  
Lamplighter Groups

We study automata groups generated by reset automata. Every lamplighter group ℤ/nℤ wr ℤ can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.

scholarly journals Groups and semigroups defined by colorings of synchronizing automata

2014 ◽  
Vol 24 (06) ◽  
pp. 773-793 ◽  
Author(s):  
Daniele D'Angeli ◽  
Emanuele Rodaro
Keyword(s):  
Finite Automata ◽  
Deterministic Finite Automata ◽  
Combinatorial Properties ◽  
Automata Groups ◽  
Synchronizing Automata ◽  
Algebraic Properties ◽  
Mealy Automata ◽  
Group A ◽  
Free Semigroups ◽  
Self Similar

In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to finitely generated synchronizing automata and characterize finite automata groups in terms of nilpotency of the corresponding DFA. Moreover, we present a decidable sufficient condition to have free semigroups in an automaton group. A series of examples and applications is widely discussed, in particular we show a way to color the de Bruijn automata into Mealy automata whose associated semigroups are free, and we present some structural results related to the associated groups.

Automata groups

2017 ◽  
pp. 194-218
Author(s):  
Derek Holt ◽  
Sarah Rees ◽  
Claas E. Roever
Keyword(s):  
Automata Groups

scholarly journals Automata groups generated by Cayley machines of groups of nilpotency class two

2021 ◽  
pp. 1-13
Author(s):  
Ning Yang
Keyword(s):  
Finite Groups ◽  
Nilpotency Class ◽  
Automata Groups ◽  
Lamplighter Groups

We build presentations for automata groups generated by Cayley machines of finite groups of nilpotency class two and prove that these automata groups are all cross-wired lamplighter groups.

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