Operations without common elements can not be generated using a finite state automata
One has to differentiate between regex in computer science and regex in real world programming languages. In compsci regular expressions are defined to only recognize regular languages, which are the same languages DFAs can recognize, thereby making DFAs and regex a descriptions of the same class of languages.
In real world application the recognition of regular languages is somewhat limiting which is the reason why many regex libraries introduce operators which allow you to recognize languages that are not regular. One such operator is recursion (?R) see here for an example using python. Notice that the language in the article is the balanced parentheses language which is a well known context free language that is not regular and thus can not be recognized by a DFA.