DFA NFA

(12 points) Assume a E . Recall that for L a set of strings over , we can define the following associated sets Assume that M = (Q, ,6.40, F) is a DFA over with L(M) = L (a) Give the formal construction of a DFA M with L(M)aL. Briefly justify each parameter (b) Apply your construction from part (a) when Ltest ba n 2 0 and n is even. A DFA (c) Give the formal construction of a NFA N, with L (N'-La. Briefly justify each parameter in the definition of M Mtest that recognizes Ltest is below. Submit the state diagram of Mtest that results. in the definition of N. Caution: Pay attention to the types of the components, especially in the transition function. You are given a DFA and are building an NFA (d) Apply your construction from part (c) when Ltest ban 0 and n is even). A DFA Mteat that recognizes Ltest is below. Submit the state diagram of Niest that results 9 State diagram for DFA Mtest