Let M = ({90, 91, 92, 93, 94, 95}, {x, y, z), qo, fs, {93, 94}) be the Deterministic Finite Automaton (DFA) with state transition function, f, defined as follows: f (qo, x) = 90 f (qo, y) = 21 f (qo, z) = 20 f(q, x) = 1 f(q, y) = 42 f(qi, z) = 42 f (q2, x) = 42 f (92, y) = 24 f (92, z) = 93 f (93, x) = 44 f (93, y) = 42 f (93, z) = 93 f (94, x) = 95 f (94, y) = 93 f (94, z) = 93 f (95, x) = 45 f(q, y) = 24 f (95, z) = 20 a) b) c) d) Draw the transition diagram for the above machine. (5 marks) Show the sequence of state transition for the input strings xxyyzz. (2 marks) Is the input string xxyyzz accepted by the DFA? Justify your answer. (2 marks) Find ONE input strings that follow the given conditions and must accepted by machine M. (6 marks) i. Length of strings is 4 and do not contains input z. ii. Length of strings is 5 and do not contains input x. Length of strings is 3, start and end with the same input string (for example: xzx). iii. You must show the sequence of state transition in each