Let M = (Q,,,q0,{q4}), where Q = {q0,q1,q2,q3,q4}, = {u,d}, and

(q0, d) = q0 (qi,d) = qi1 if i != 0

(q4, u) = q4 (qi,u) = qi+1 if i != 4

1. (a) [2 points] This DFA describes the operation of a commonplace object. What is this object? Hint: The fact that I used u and d should give you a clue.

2. (b) [4 points] Describe L(M). You may give an informal description in terms of the object mentioned in part (a) of this problem.

3. (c) [4 points] Give the state diagram of this machine.

1. Let M = (Q, 2,8,90, {94}), where Q = {90,91,92, 93, 94}, { = {u, d), and 8(qo, d) = 90 8(qi, d) = qi-1 if i = 0 8(94, u) = 24 8(qi, u) = qi+1 if i + 4 (a) [2 points] This DFA describes the operation of a commonplace object. What is this object? Hint: The fact that I used u and d should give you a clue. (b) [4 points] Describe L(M). You may give an informal description in terms of the object mentioned in part (a) of this problem. (c) [4 points] Give the state diagram of this machine