Let M = be a finite state machine with |S| = n, and let 0 f.

Let M =

be a finite state machine with |S| = n, and let 0 ˆˆ f.
(a) Show that for the input string 0000. .. , the output is eventually periodic.
(b) What is the maximum number of 0's we can input before the periodic output starts?
(c) What is the length of the maximum period that can occur?

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