On the periodicity of the sequence of states of an automaton corresponding to the initial state and the input periodic sequence

We introduce a formalisation of the intuitive notion of almost periodicity of elements of a finite alphabet, the measure of approximate period of this sequence. We obtain a lower bound of the measure of approximate period of the sequence of states of an automaton for a given initial state and a given periodic input sequence. On the base of this estimate, we obtain a lower bound for the measures of approximate periods of output sequences of automata modelling the functioning of shift registers.