1. (20 points) Construct a NFA for regular expression ab[ab]*ba. Convert the NFA to the DFA. 2. (30 points) Minimize the number of states of the DFA defined by the following transition graph. a 3. (50 points) Minimize the number of states of the DFA defined by the following transition table. The initial state is O and the final states are 3 and 8. b 0 1 2 1 3 5 2 5 4 3 1 2 6 8 5 2 6 6 7 5 7 2 4 1 4 8 N00