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Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection,and complement.

  1. $\{0^{n}1^{m}0^{n}|m,n\geq 0\}$
  2. $\{0^{m}1^{n}|m\neq n\}$
  3. $\{w|w\in\{0,1\}^{*}  \text{is not a palindrome}\}$
  4. $\{wtw|w,t\in\{0,1\}^{+}\}$
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