Is the Complement of (0^n)(1^n)^m Non-Context-Free?

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The discussion centers on proving that the complement of the language L = {((0^n)(1^n))^m | m,n are integers greater than zero} is non-context-free. A participant suggests using the Pumping Lemma as a method for this proof. However, it is later clarified that the complement of the language is actually a context-free language (CFL), indicating that the initial assumption about its non-context-freeness was incorrect. This highlights the importance of thoroughly analyzing language properties and the applicability of theoretical tools like the Pumping Lemma in formal language theory.
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I was looking for a way to prove that the complement of the following language is non-context-free:
L={((0^n)(1^n))^m | m,n are integers greater than zero}

Thank you in advance
 
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I found out what I was missing. The complement is indeed CFL
 

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