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Use the pumping lemma for regular languages to prove that the following language is not regular....

Use the pumping lemma for regular languages to prove that the following language is not regular.

{ 0n1x0x1n | n >= 0 and x >= 0 }

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Answer #1

Let us assume that L is a regular language. Let us assume that m = 0n1x0x1n belongs to L and u = 0n, v = 1x and w = 0x1n.

Clearly, |uv| <= n and |v| >= 1.

Now, for i = 2, uviw = 0n12x0x1n

Clearly, uv2w does not belong to L and hence, our assumption was wrong, This means that L is not regular.

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