I need #2 please. Thanks.

1. Define a nondeterministic finite automaton for the regular experssion a* (bab)*a* using the Thompson NFA construction. 2. Using the algorithm presented in class, convert your NFA from Problem (1) into an equivalent DFA. Nondeterminstic Finite Automata Equivalence of NFA's and DFA's. Let N = (Q, E, F, 90, 8) be a nondeterminstic finite automaton which accepts the language L. We construct the equivalent determinstic finite automaton M = (Q', E, F, 9%, S') as follows: 1. Q' = P(Q) 2. For every state Re Q' and symbola e 2, let 8'(R. a) be defined as: {qe Q9 Es(r, a)) for some reR} where E(R) = {919 can be reached from R by following zero or more e transitions}. 3. 96 = E({90}) 4. F' = {RE QRAF# } For every symbol of a given input string, it is clear that M enters a state corresponding to the states that N might be in, and hence the construction is necessarily correct. Nondeterminstic Finite Automata Definition (Nondeterministic Finite Automata) A nondeterministic finite automaton is a 5-tuple of the form (Q, 2, F, 90, 8) where: . Q is a finite set of states is an input alphabet F C Q is the set of final states 90 Q is the initial state 5:QxEg P(Q) is the transition function and E = EU {E}. Deterministic Finite Automata Definition (Deterministic Finite Automata) A deterministic finite automaton is a 5-tuple of the form (Q, E, F, 90, 8) where: Q is a finite set of states I is an input alphabet FCQ is the set of final states 90 Q is the initial state 5:Qx? Q is the transition function