Let X = {a, b} and Y = {0, 1} and consider : X* Y where: (a) B(x) = { 1 if the numbers of a's and b's in x are equal, 0 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]B and the functions Bob (x e X*). (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 M(B). Let X = {a, b} and Y = {0, 1} and consider : X* Y where: (a) B(x) = { 1 if the numbers of a's and b's in x are equal, 0 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]B and the functions Bob (x e X*). (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 M(B)