[Solved]: Give an example of a non-regular language $L$ such that $L^*$ is regular

Problem Detail: 

I can't think of an example of a non-regular language $L$ such that $L^*$ is regular. . Any help ?

Asked By : Altaïr

Answered By : R B

Define $L=\{a^nb^n|n\in \mathbb N\}\cup \{a,b\}$

It's not hard to see that while $L$ is not regular, $L^*=\Sigma^*$.

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Question Source : http://cs.stackexchange.com/questions/35350

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