Fragile words and Cayley type transducers

Daniele D'Angeli, Emanuele Rodaro
2018 International Journal of Group Theory  
We address the problem of finding examples of non-bireversible transducers defining free groups, we show examples of transducers with sink accessible from every state which generate free groups, and, in general, we link this problem to the non-existence of certain words with interesting combinatorial and geometrical properties that we call fragile words. By using this notion, we exhibit a series of transducers constructed from Cayley graphs of finite groups whose defined semigroups are free,
more » ... groups are free, and thus having exponential growth.
doi:10.22108/ijgt.2017.100358.1398 doaj:5c90be21f1f643f3ab6544d3bc972120 fatcat:xqziqh3lura4bmg27ee2pn54cq