Prove that L = {ww | w ∈ {0, 1}∗} is not regular
Assume that L is regular. Let p be the pumping length guaranteed by the Pumping Lemma. Take w =0p10p1 . Clearly, w ∈ L, and |w| ≥ p. We need to show that for any partition w = xyz, with |xy| ≤ p, and y≠∈, there exists i ≥ 0, such that xyiz ∉ L. […]