EXERCISE 4 Show that {xcx" | x e {a, *) is not regular. Hint: Copy the proof ofTheorem 11.2- only minor alterations are needed Theorem 11.2: x is not regular for any alphabet with at least two symbols Proof: Let M2(Q, , 8, %, F) be any DFA with 1 1 2; we will show that L(M) {xx/J. The alphabet contains at least two symbols; call two of these a and b. Consider the behavior of M on an arbitrarily long string of as. As it reads the string, M visits a sequence of states: first "(%-c), then *(%-a), then "(%-aa), and so on. Eventually, since M has only finitely many states, it must revisit a state; that is, there must be some i and j with i