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We define the minimal words language of $L, \min(L)$, to be the language of all words in $L$ that don't have any prefix in $L$.

Assume $L$ is regular language. I need to prove by building an automaton that $\min(L)$ is regular.

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Welcome at math.SE! You can use $\LaTeX$ here, e.g. $L$ would look like $L$, for more see FAQ, it is very helpful. Also, could you please fix the spelling of your post (e.g. use the browser build-in spellchecker)? Some people might find the quality of your question insulting. – dtldarek Nov 30 '12 at 17:08
Look, for example, at the edits I just made. Click on the link after the word "edited" and then look at the source, by clicking on "source". – Rick Decker Nov 30 '12 at 17:11

Hint: Consider a deterministic automaton, if you happen to be at the accepting state, anything that comes later should send you to the "trash" state.

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