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In a question, it is given that L is a finite language over the unary alphabet and L+ is not regular. We know that L+ = LL* Since L is finite, it must be regular because all finite languages are regular. If L is regular L* is also regular. Then how can be L+ not regular? It is the concatenation of two regular languages. Where am I wrong?

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it is given that L is a finite language over the unary alphabet and L+ is not regular.

That's impossible. Since $L$ is finite, it is regular. Since $L$ is regular, $L^+ = L L^*$ is regular. See, e.g., https://en.wikipedia.org/wiki/Regular_language#Closure_properties.

You're not wrong; you are right.

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  • $\begingroup$ The more interesting question is what was intended, i.e., what modification to the statement would make it non-stupid. $\endgroup$ – Rick Decker Mar 7 '18 at 14:43
  • $\begingroup$ Also, note that the unary alphabet doesn't give us anything new. $\endgroup$ – Rick Decker Apr 3 '18 at 12:49

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