very urgent,thank you

1. (10 + 10 20 points) You are given 2 DFAs M (Q1,9, 81,910, Fi) and M2 (Q2, 2, 82, 920, F2). We want to construct a DFA M = (0, 2, 8,40,F) recognizing the concatenation L(M) L(M2). One solution would be as follows. Connect cach accept state of M to the start state of M2 by an e-move, and make the accept states of M non-accepting. This is an NFA N = (Q',9,8,46, F') accepting L(M) L(M2). Now transform this NFA into an equivalent DFA. If |Q11 = ky and Q2] = k2, then 2k11 k2 would be an obvious upper bound on the number of states of such a DFA M. We can actually do much better, because many states of the DFA M obtained with the full subset construction are not reachable from the start state. (a) Identify a large subset of the power set of Q' that are states of M not reachable from the start state. (b) Give a good upper bound on the number of reachable states of the DFA M? 1. (10 + 10 20 points) You are given 2 DFAs M (Q1,9, 81,910, Fi) and M2 (Q2, 2, 82, 920, F2). We want to construct a DFA M = (0, 2, 8,40,F) recognizing the concatenation L(M) L(M2). One solution would be as follows. Connect cach accept state of M to the start state of M2 by an e-move, and make the accept states of M non-accepting. This is an NFA N = (Q',9,8,46, F') accepting L(M) L(M2). Now transform this NFA into an equivalent DFA. If |Q11 = ky and Q2] = k2, then 2k11 k2 would be an obvious upper bound on the number of states of such a DFA M. We can actually do much better, because many states of the DFA M obtained with the full subset construction are not reachable from the start state. (a) Identify a large subset of the power set of Q' that are states of M not reachable from the start state. (b) Give a good upper bound on the number of reachable states of the DFA M