Let be an alphabet, and let x * where Ix-n. Recall that xR-x[n]x[n-1] x[1] is the reverse of x. Let A C *. Define the reverse of A as AR-{xR x E A} . Prove that the class of regular languages is closed under the reverse operation, i.e., prove that if A is regular, then A is regular Do this by showing how to convert a DFA D into an NFA N such that L(N) L(D)R, Hint: N should simulate running D backwards". guess an accept state that D could end up in, and when reading a symbol b E , guess what state(s) D could have been in prior to reading b. With proper guessing on a string in L(D)R, N should end up back at the start satc of D Let be an alphabet, and let x * where Ix-n. Recall that xR-x[n]x[n-1] x[1] is the reverse of x. Let A C *. Define the reverse of A as AR-{xR x E A} . Prove that the class of regular languages is closed under the reverse operation, i.e., prove that if A is regular, then A is regular Do this by showing how to convert a DFA D into an NFA N such that L(N) L(D)R, Hint: N should simulate running D backwards". guess an accept state that D could end up in, and when reading a symbol b E , guess what state(s) D could have been in prior to reading b. With proper guessing on a string in L(D)R, N should end up back at the start satc of D