Question 1 Let LCE* be a regular language over some alphabet E. The Kleene-closure L* of L is given by L* = { V₁ V₂ Vn | n ≥ 0, V₁, V2, ..., Un € L}. (Q, E, 6, qo, F) satisfies L(D) L*. (a) Suppose DFA D such that L(N) = = L. Construct an NFA N = (Q', Σ, δ', 4%, F') (b) Prove by induction on n that each word v₁v2 Un with n ≥ 0, V₁, V2, ..., Un € L is accepted by the NFA N proposed in item (a). (c) Prove that each word accepted/recognized by the NFA N proposed in item (a) is a word of the language L*.

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