I have a problem and I don't understand it. I need to find a language $L$ (using the alphabet $\Sigma = \{a,b\}$) The problem is that $L$ can't be $\{a,b\}^*$ or $\{\epsilon\}$ and it must be equal to $L^*$. Any ideas? Sorry if my english is not good.
2026-03-25 17:37:52.1774460272
How to find a language L that is equal to L*??
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How about defining $L=\{\epsilon, a, aa, aaa, aaaa, \ldots\}$? This is the set of all strings made only of the letter $a$.
The Kleene star language $L^*$ consists of any number of strings from $L$ concatenated together. But if you concatenate any strings made of only $a$ characters together, the result will also be a string made of $a$ characters. Hence $L=L^*$.