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InfluxDB
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The "Papers" section on re2c's web site continues Laurikari's work: http://re2c.org/
... but I haven't found them particularly accessible. And it's not clear it's a viable strategy in a general purpose regex engine. Namely, I'm not sure how much bigger it makes the DFA.
Also, AFAIK, these are DFAs. They are different theoretical structures with explicitly more power.
> and then an NDFA is used to match a third time, to extract the capture groups.
That's the PikeVM. It's an NFA simulation. Although it uses additional storage and is otherwise more computationally powerful than just a plain NFA.