A Characterization of Those Automata That Structurally Generate Finite Groups
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چکیده
Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit—that is, where every cycle in the underlying directed graph is a sink component—generates a finite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper.
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تاریخ انتشار 2014