What is this? I'm so curious but nothing of this rings a bell with me. I mean I know what a regular expression is, and I've formatted several USBs to FAT32, but DFAs and everything in between have me Googling like crazy, still in the dark though.
The file system could work around that by creating new unique directories whenever you write any file to an empty directory, but that would require it to keep the regular expression it represents around, and would fill up the file system quite rapidly.
Even automata based regex engines don't usually build up a full DFA, since the size of the DFA may be exponential in the size of the regex. Instead, an NFA similation might be used, or a hybrid NFA/DFA that builds the DFA during match time, but typically doesn't build out the full DFA.