Earlier quoted context omitted.
I mean, the whole point of regexes (not to be confused with PCREs) is that any given regex is isomorphic to some canonical finite state machine. It is, specifically speaking, a tiny description of an FSM over the alphabet of ASCII characters (or whatever charset you're using). Interestingly, regexes/FSMs are (IIRC) the most powerful class of machines for which equivalence is decidable. So if you give me any two regex…
Isn't it possible to decide the equivalence of deterministic pushdown automata? Wouldn't DPDAs be considered more powerful than FSMs due to the addition of a stack? Wikipedia [1] shows there's a paper called "The equivalence problem for deterministic pushdown automata is decidable" that won the Gödel Prize is 2002. I haven't read the paper nor do I currently have access to it though. [1] https://en.wikipedia.org/wiki…
http://link.springer.com.sci-hub.cc/chapter/10.1007/3-540-63...
It was initially published in 1997.