automatic groups
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Author(s):  
DMITRY BERDINSKY ◽  
MURRAY ELDER ◽  
JENNIFER TABACK

Abstract We extend work of Berdinsky and Khoussainov [‘Cayley automatic representations of wreath products’, International Journal of Foundations of Computer Science27(2) (2016), 147–159] to show that being Cayley automatic is closed under taking the restricted wreath product with a virtually infinite cyclic group. This adds to the list of known examples of Cayley automatic groups.



2019 ◽  
Vol 28 (2) ◽  
pp. 282-292
Author(s):  
Konstantinos Zervoudakis ◽  
Konstantinos Mastrothanasis ◽  
Stelios Tsafarakis


2019 ◽  
Vol 793 ◽  
pp. 193-195
Author(s):  
Benjamin Blanchette
Keyword(s):  




2017 ◽  
Author(s):  
Mikael Vejdemo-Johansson

The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for automatic groups with normal form recognizing automata that recognize a single normal form for each group element, and are at most context free in complexity: context free grammars can be translated into algebraic systems of equations, whose solutions represent generating functions of their corresponding non-terminal symbols. This approach allows us to seamlessly introduce weightings on the growth function: assign different or even distinct weights to each of the generators in an underlying presentation, such that this weighting is reflected in the growth function. We recover known growth functions for small braid groups, and calculate growth functions that weight each generator in an automatic presentation of the braid groups according to their lengths in braid generators.



2017 ◽  
Author(s):  
Mikael Vejdemo-Johansson

The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for automatic groups with normal form recognizing automata that recognize a single normal form for each group element, and are at most context free in complexity: context free grammars can be translated into algebraic systems of equations, whose solutions represent generating functions of their corresponding non-terminal symbols. This approach allows us to seamlessly introduce weightings on the growth function: assign different or even distinct weights to each of the generators in an underlying presentation, such that this weighting is reflected in the growth function. We recover known growth functions for small braid groups, and calculate growth functions that weight each generator in an automatic presentation of the braid groups according to their lengths in braid generators.



2017 ◽  
pp. 125-149
Author(s):  
Derek Holt ◽  
Sarah Rees ◽  
Claas E. Roever
Keyword(s):  


2016 ◽  
Vol 27 (02) ◽  
pp. 147-159 ◽  
Author(s):  
Dmitry Berdinsky ◽  
Bakhadyr Khoussainov

We construct the representations of Cayley graphs of wreath products using finite automata, pushdown automata and nested stack automata. These representations are in accordance with the notion of Cayley automatic groups introduced by Kharlampovich, Khoussainov and Miasnikov and its extensions introduced by Elder and Taback. We obtain the upper and lower bounds for a length of an element of a wreath product in terms of the representations constructed.



2015 ◽  
Vol 7 (2) ◽  
Author(s):  
Jennifer Taback ◽  
Sharif Younes

AbstractThe definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to 𝒞-graph automatic by Elder and the first author raise the question of whether Thompson's group



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