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This question already has an answer here:

Given a string, take all of its substrings (including the empty string). For example, given $abc$, we can form a set $\{\emptyset, a, b, c, ab, bc, abc\}$.

Given a regular language, take all the substrings of each of its strings, and form a language thereof. I wonder if the formed language is still regular?

Btw, is there a name for such an operation? In some sense, it is similar to taking the powerset of a set.

Thanks.

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merged by Gilles Jun 9 '14 at 23:55

This question was merged with Regularity of “middles” of words from regular language because it is an exact duplicate of that question.

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