Geodesic
On the periodicity of the sequence of states of an automaton corresponding to the initial state and the input periodic sequence
Diskretnaya Matematika, Tome 14 (2002) no. 2, pp. 54-64.

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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. 
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A. V. Babash. On the periodicity of the sequence of states of an automaton corresponding to the initial state and the input periodic sequence. Diskretnaya Matematika, Tome 14 (2002) no. 2, pp. 54-64. http://geodesic.mathdoc.fr/item/DM_2002_14_2_a5/

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