D'Angeli, D., Rodaro, E. (2018). Fragile words and Cayley type transducers. International Journal of Group Theory, 7(3), 95-109. doi: 10.22108/ijgt.2017.100358.1398
Daniele D'Angeli; Emanuele Rodaro. "Fragile words and Cayley type transducers". International Journal of Group Theory, 7, 3, 2018, 95-109. doi: 10.22108/ijgt.2017.100358.1398
D'Angeli, D., Rodaro, E. (2018). 'Fragile words and Cayley type transducers', International Journal of Group Theory, 7(3), pp. 95-109. doi: 10.22108/ijgt.2017.100358.1398
D'Angeli, D., Rodaro, E. Fragile words and Cayley type transducers. International Journal of Group Theory, 2018; 7(3): 95-109. doi: 10.22108/ijgt.2017.100358.1398
2Dipartimento di Matematica, Politecnico di Milano, Milano, Italia
Abstract
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.
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