Let f = 0 = {0, 1}. (a) Construct a state diagram for a finite state machine that recognizes each occurrence of 0000 in a string x ∈ f. (Here overlapping is allowed.) (b) Construct a state diagram for a finite state machine that recognizes each string x ∈ f* that ends in 0000 and has length 4k, k ∈ Z+. (Here overlapping is not permitted.)