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Reading Chomsky hierarchy …
… I know regexp can’t parse type-2 grammars (context-free grammars), and also type-1 and type-0.
Can regular expressions parse/catch ALL type-3 grammars (regular grammars)?
Yes, provided they support alternation, concatenation, and the Kleene star. This is the case for regexes of the PCRE (Perl/Java/JavaScript/PHP/…) type: alternation is implemented by
((...)|(...)), concatenation by(...)(...), and the Kleene star by(...)*. (There are a few other details — in most of these languages you need to use something like\Aand\zto indicate “start-of-string” and “end-of-string”, which in a regular grammar is taken for granted — but that’s the idea.)But not everything called a “regular expression” in a programming context necessarily has all of the above; for example, POSIX Basic Regular Expressions supports only a very limited form of alternation, where all “branches” of the alternation consist of a single character (e.g., whereas PCREs has both
(a|b|c)and the special-case-equivalent[abc], POSIX BREs only have[abc], so can’t express something like(ab|c)).