On the Periodic Equivalents of Finite Automata

This correspondence deals with the problem of finding periodic equivalents of finite automata, The idea of periodic equivalent is a generalization of the concept of strictly periodic equivalent studied in [4]. In this correspondence some essential properties of periodic equivalents of finite automata are investigated. Further-more, the concept of strong kernel of automaton is introduced and some connections of strong kernels with periodic equivalents are presented. Finally, the algorithm for determining minimal periodic equivalents of automata is given.