JNTU B.Tech III AUTOMATA AND COMPILER DESIGN Previous Question Paper (August - 2022 - R13)

To convert an NFA to a DFA, we use the subset construction algorithm. Given an NFA with states {q0, q1, q2} and transitions, we define the DFA states as subsets of the NFA states. Starting with the epsilon-closure of the initial state, we compute the transition for each input symbol by finding the union of all reachable states in the NFA. For example, if the NFA has transitions δ(q0, a) = {q0, q1}, the DFA state {q0} on input 'a' transitions to the DFA state {q0, q1}. We repeat this process for every newly created subset until no new states are generated. Finally, any DFA state containing an NFA final state is marked as a final state in the DFA.

To construct an NFA for the regular expression r = (a + bb)*(ba* + b), we use Thompson's construction method by building smaller NFAs for each sub-expression and connecting them using epsilon transitions.

1. Construct the NFA for (a + bb) by creating a union of the NFA for 'a' and the NFA for 'bb' (a sequence of two 'b' transitions), then apply the Kleene star closure.
2. Construct the NFA for (ba* + b) by creating a union of the NFA for 'ba*' (a 'b' transition followed by 'a' star closure) and the NFA for 'b'.
3. Concatenate the NFA from step 1 with the NFA from step 2 using an epsilon transition to represent the concatenation operator.
4. The resulting NFA will have a start state with an epsilon transition to the Kleene star structure, which then transitions to the final part of the expression, ending in an accepting state.