You are right, I should be more precise with my terminology. By "regexp" I meant "regular expression". Regardless, neither term implies implementation as a DF

You are right, I should be more precise with my terminology. By "regexp" I meant "regular expression". Regardless, neither term implies implementation as a DFA, however regular expressions, and the subset of regexps which are equivalent to them, can and should be compiled to an optimized DFA.