The languages and their expressions are getting more and more complex.
I don't quite understand why the language L that has an equal number of 0s and 1s violates the pumping lemma. Say for example, u = 1, v = 01, w = 0 and p = 3, then uv^kw \in L still.
Ah, I know where I got it wrong! The example I gave is just a specially case in L, more generally it doesn't hold. For example u = 01, v = 01, w = 0 and p = 3, then uv^kw not \in L.
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