On the Existence of a Periodic Analog of a Finite Connected Automaton

The solution of the problem of the existence of an analog with periodic-variable structure of a given fixed-structure connected automaton is presented. Using a Boolean approach, a necessary and sufficient condition for the existence of the periodic analog is proven, and an algorithm that enables us to actually find this analog is given. The saving of the memory capacity needed for the construction of a given automaton is the main interest of the existence of a periodic analog.