Cycle indices of an automaton
A. A. Letunovskii · Discrete Mathematics and Applications · 2013
The notion of cycle indices of an automaton is introduced as a pair of positive parameters (b, q) effectively evaluated by the automaton. It is shown that the totality of periods of constant automata which may be represented as superpositions of a given automaton, Boolean functions, and the delay element, coincides with the variety of divisors of the members of the geometric progression b, bq, bq 2 ,... This suggests an algorithm for checking the expressibility of constant automata, as well as a theorem on the verification of the expressibility of the totality of all automata with a limited number of states.