If L is any regular language, let L2/3 be the language in which the middle thirds of strings in L are removed:

L2/3 = { xz | xyz in L and |x| = |y| = |z|, for some y}.

Prove that if L is regular, L2/3 is not necessarily regular.

HINT: A good (clever) counter-example might do the trick. If E = (000)* is regular (it is after all a regex), is E2/3? What if we used a marker, i.e., what if E = (101)* or (100)* or (101)*?