I don't think so. There's a reason why exactly zero popular regex engines build full DFAs. (Sometimes small DFAs are built in cases where you know they'll be very small or enforce a tight bound, but even then, the DFA is typically used as a prefilter rather than a regex engine unto itself.)
There are plenty of regex engines that do build full DFAs, but they're either relegated to the work of research or niche areas. re2c, for example, is an excellent regex engine that translates regex syntax into DFA source code. It thus has procedures for compilation and execution, but it is not what I would call a "general purpose" regex engine.
As another example, if I were to make Rust's regex crate use quadratic (or far worse, exponential) compilation, I'm pretty sure I'd have many upset users. (Now, I could use quadratic or even exponential compilation in cases where I'm sure that the absolute wall clock time won't be disagreeable, but I think it's safe to exclude such things for the purposes of this discussion.)
Even for DFAs that don't take exponential time, Unicode means that DFAs get obscenely big. \pL, for example, is 279 states and uses 143K of memory. And it takes around 8ms to compile on my machine. 1ms is already pushing it.
> Are you sure that a less naive approach doesn't exist?
Pretty sure. I'm not an expert in the theory either. I'm just aware of most of it. And I'm totally unaware of anyone who has overcome the practical engineering challenges of things like complement and intersection.
Vcsn link: https://www.lrde.epita.fr/wiki/Vcsn
I don't know, maybe just don't make grand pronouncements about regex engines if you aren't actually familiar with how they're implemented and the engineering tradeoffs in play?
> The bottom line is that if you have an NFA with N states and you take its complement (how do you do that without first converting it to a DFA?), then you could wind up with an NFA containing a number of states exponential in N.
Are you sure that a less naive approach doesn't exist? Genuinely asking, I'm not an expert. I don't quite remember the contents, but I know there are some papers with extensions to Antimirov derivatives (see updated upthread comment) that support taking the complement of an expression.