Abstract
The properties of endomorphisms and automorphisms of a finite, deterministic automatonA related to the smallest input-independent partition on the set of internal states ofA are investigated. The setH d of all thed-endomorphisms ofA defined here, as well as the setG d of all thed-automorphisms ofA, are studied in detail. It is proved thatH d forms a polyadic semigroup, whileG d forms a polyadic group. Connections betweenG d and the groupG(A) of all the automorphisms ofA are examined. The upper bound for the cardinality ofG d is given.
Finally, by means of the theory ofd-automorphisms, some problems of the theory of strictly periodic automata are solved; in the first place, the necessary and sufficient condition for the reducibility of an arbitrary strictly periodic automation is given.
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Grzymala-Busse, J.W. On the endomorphisms of finite automata. Math. Systems Theory 4, 373–384 (1970). https://doi.org/10.1007/BF01704080
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DOI: https://doi.org/10.1007/BF01704080