Problem Detail: I am having hard time solving the following problem.
Are there any languages for which $$ overline{L^*} = (overline{L})^* $$
Assuming $emptyset^* = emptyset$, if I consider $Sigma = {a}$ and L = $Sigma^*$, I get that $L^* = L$ and that $overline{L^*} = emptyset$. For the right side I get $overline{L} = emptyset$ and $(overline{L})^* = emptyset$. Thus, both sides are equal. Is it true that $emptyset^* = emptyset$?
Asked By : user118837
Answered By : Rick Decker
Hint: The star of a language always contains the empty string. The complement of a language containing the empty string never does. With that in mind, look at the left and the right hand sides of your proposed equality.
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Question Source : http://cs.stackexchange.com/questions/21544
