Abstract:We introduce the notion of the automatic logarithm LogA(B) of a finite initial Mealy automaton B, with another automaton A as the base. It allows one to find for any input word w a power n such that B(w)=An(w). The purpose is to study the expanding properties of graphs describing the action of the group generated by A and B on input words of a fixed length interpreted as levels of a regular d-ary rooted tree T. Formally, the automatic logarithm is a single map LogA(B):∂T→Zd from the boundary of the tree to the… Show more
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