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Question: first give the state diagram for the nfa that recognizes...

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First, give the state diagram for the NFA that recognizes the language below using no more than 3 states. Next, use the powerset construction from the proof of Theorem 1.39 in the book to convert the NFA into a DFA. If there are any unneeded states or states that can be combined, you may simplify your DFA, but show your DFA’s state diagram before and after simplification.

6. First, give the state diagram for the NFA that recognizes the language below using no more than 3 states. Next, use the powerset construction from the proof of Theorem 1.39 in the book to convert the NFA into a DFA. If there are any unneeded states or states that can be combined, you may simplify your DFA, but show your DFAs state diagram before and after simplification. 10 points o we\a, b aa is a suffix ofvw

Theorem 1.39 states: Every nondeterministic finite automaton has an equivalent deterministic finite automaton

Proof:

PROOF Let N-(Q, ,,o, F) be the NFA recognizing some language A We construct a DFA M-(Q, Σ, δ, qo, F) recognizing A. Before doing the full construction, lets first consider the easier case wherein N has no ε arrows. Later we take the ε arrows into account. Every state of M is a set of states of N. Recall that P(Q) is the set of subsets of Q 2. For R e Q, and a E Σ, let δ(R, a)-{0€ Qlq E δ(na) for some r E R} If R is a state of M, it is also a set of states of N. When M reads a symbol a in state R, it shows where a takes each state in R. Because each state may go to a set of states, we take the union of all these sets. Another way to write this expression is rER M starts in the state corresponding to the collection containing just the start state of N. 4. F-RE Q R contains an accept state of N. The machine M accepts if one of the possible states that N could be in at this point is an accept state

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