7 Let X a, b and Y 0, 1 and consider B X Y where (a) B(x) 1 if the numbers of a's and b's in x are equal, O otherwise (b) B(x) 1 if x contains an odd number of the subsequence abab, O otherwise (i) For each of the two functions above, describe the Nerode equivalence classes x and the functions Bob (x EX) (ii) For each of the two functions above, if is not finite state realizable, prove it if is finite state realizable give a transition graph for the reduced machine MB or MB) 7 Let X a, b and Y 0, 1 and consider B X Y where (a) B(x) 1 if the numbers of a's and b's in x are equal, O otherwise (b) B(x) 1 if x contains an odd number of the subsequence abab, O otherwise (i) For each of the two functions above, describe the Nerode equivalence classes x and the functions Bob (x EX) (ii) For each of the two functions above, if is not finite state realizable, prove it if is finite state realizable give a transition graph for the reduced machine MB or MB)

Question

7  Let X    a, b  and Y    0, 1  and consider B  X  Y where  (a) B(x)     1 if the numbers of a's and b's in x are equal, O otherwise  (b) B(x)     1 if x contains an odd number of the subsequence abab, O otherwise  (i) For each of the two functions above, describe the Nerode equivalence classes  x  and the functions Bob (x EX)  (ii) For each of the two functions above, if is not finite state realizable, prove it  if is finite state realizable give a transition graph for the reduced machine MB or MB)  7  Let X    a, b  and Y    0, 1  and consider B  X  Y where  (a) B(x)     1 if the numbers of a's and b's in x are equal, O otherwise  (b) B(x)     1 if x contains an odd number of the subsequence abab, O otherwise  (i) For each of the two functions above, describe the Nerode equivalence classes  x  and the functions Bob (x EX)  (ii) For each of the two functions above, if is not finite state realizable, prove it  if is finite state realizable give a transition graph for the reduced machine MB or MB)

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Question

7. Let X = {a, b} and Y = {0, 1} and consider B: X+ Y where: (a) B(x) = { 1 if the numbers

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