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[Solved]: Concatenation of $a^p$ and $a^m$ where $p$ and $m$ are primes, is irregular?

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I believe that the concatenation $a^pa^m$ where $p$ and $m$ are primes is not regular, since I can show that $a^p$ is not regular using the pumping lemma, therefore there is no NFA for the 1st part, therefore the concatenation cannot be regular (I.e. there is no NFA to do the lambda transition)

Is the above reasoning correct?

Asked By : JohnMadon1234567890

Answered By : JohnMadon1234567890

No, non regular languages are not closed under the concatenation, therefore the premise wrong. See Proving that non-regular languages are closed under concatenation for a counterexample.

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