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If $L^2$ is regular. Does that imply L is regular.


I think L need not be regular. But I can't find any example where L is not regular but $L^2$ is regular.

My teacher told me an example where L={$0^k$ | k is composite} clearly L is not regular. But he claims that $L^2$ is regular. I don't know why it is regular? Please help.

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    $\begingroup$ Your teacher gave good example. You should just write out some words in $L^2$ to see what $L^2$ is actually equivalent to. That's the hint. $\endgroup$ – Apiwat Chantawibul Sep 2 '19 at 11:17
  • $\begingroup$ I added an answer to the other question, explaining why your teacher's claim is true. $\endgroup$ – David Richerby Sep 2 '19 at 18:56