(Answered) Prove that for each regular set a sube 0 1lowastit holds

Engineering

Prove that for each regular set A ⊆ {0, 1}∗it holds thatLA = {x | (∃y ∈ {0, 1}∗)[|y| = 4|x| and xy ∈ A]}is regular. Do so by letting M = (Q, {0, 1}, δ, q0, F) be a DFA accepting A and then specifyclearly-via specifying its components, (Q0, {0, 1}, δ0, q00, F0)-an NFA accepting LA. Youdo not have to include a proof of the correctness of your construction, but it should in factbe correct.

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