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Theory of Computation

Let x be an element of Σ+ be a word. Show that for all such x, the language L=x* is regular. Give an example of x such that the language:

L subscript 2/3 = {uw l there exists a y an element of L, y=uvw, l u l = l v l = l wl }

is not regular. Prove your answer.

(note: l l is equal to the length)

Please see the attached file for a more concise view of the problem.

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Theory of Computation is embedded.