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Fragile words and Cayley type transducers. (English) Zbl 1446.20043
Summary: 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.
MSC:
20E08 Groups acting on trees
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
68Q45 Formal languages and automata
Software:
AutomGrp
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