Does every regular language have a proper regular superset? or proper subset?
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Does every regular language have a proper regular superset? or proper subset?
For a fixed alphabet, no: there is at least one regular language for which there is no regular proper subset, and at least one regular language for which there is no regular proper superset.
Hint1: the definition of these languages is incredibly basic, such that each can be fully described in no more than five and three words (two and one, if you leave out articles, prepositions, “language” and “strings”).
Hint2: the fact that you’re talking about regularity and languages instead of any property for any kind of set isn’t terribly relevant to answering this question. All that’s important is that, for a fixed alphabet, the sets with this property include two very important sets, which when identified, answer this question.