Question: For any set of strings A , define the set MiddleThirds A = { y I 3 x , z Ixl = Iyl = Izi

For any set of strings A, define the set MiddleThirds A ={y I 3x, z Ixl = Iyl = Izi and xyz in A}. For example, MiddleThirds{ f, a, ab, bab, bbab, aabbab}={f, a, bb}. Show that if A is regular, then so is MiddleThirds A.

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