Fragile words and Cayley type transducers
Daniele D’Angeli, Emanuele Rodaro · Virtual Community of Pathological Anatomy (University of Castilla La Mancha) · 2018
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, and thus having exponential growth.