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 setHd of all thed-endomorphisms ofA defined here, as well as the setGd of all thed-automorphisms ofA, are studied in detail. It is proved thatHd forms a polyadic semigroup, whileGd forms a polyadic group. Connections betweenGd and the groupG(A) of all the automorphisms ofA are examined. The upper bound for the cardinality ofGd 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.