I am interested in the following questions and would be grateful if anyone could give me hints or point me to articles:
1) Given a regular language $L$, what are its regular sublanguages $L'\subseteq L$, i.e. how to enumerate all regular $L' \subseteq L$ for a given regular language $L$.
2) Could every regular sublanguage $L'$ of a regular language $L$ be written as $L' = L''\cap L$ with $L''$ regular
3) Given a arbitrary language, is it decidable if it is regular (of course one could compute it's syntactic monoid, but this computation could take on forever if the language is not regular)