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. $\endgroup$ Commented Mar 7, 2018 at 14:43
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$\begingroup$ Also, note that the unary alphabet doesn't give us anything new. $\endgroup$ Commented Apr 3, 2018 at 12:49