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*.

Q: 3. Show that the following language A is not regular using the pumping lemma. {0n1m+nom | m, n >0} A…

A:

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A: Given :

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A: The Answer is in Below Steps

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A: Showed that the given language are pairwise distinguishable