EDIT: Looks like the original linked page was first published in 2001[2].
[0] https://github.com/google/re2
[1] https://swtch.com/~rsc/regexp/regexp1.html
[2] https://web.archive.org/web/*/http://perl.plover.com/NPC/
As far as the theoretical term is concerned, regular expressions with backreferences are not regular expressions. The power that backreferences add comes at great cost: in the worst case, the best known implementations require exponential search algorithms, like the one Perl uses. Perl (and the other languages) could not now remove backreference support, of course.
Cox then proposes a hybrid engine that can be quicker when capture groups aren't needed. TCL has this sort of hybrid implementation, http://wiki.tcl.tk/396. It's worst case performance won't be big-O better than Perl's for pathological cases that require backtracking.
If P no more or less equals NP today than in 2001, the article's conclusion has not lost correctness.
Capture groups aren't the same thing as backreferences. You can do capturing groups fine in linear time (or at least, something close to linear time).
CHAPTER 5 Pattern Matching
Fancy Patterns - Alternate Engines
Starting with v5.10, you can even swap out Perl’s entire regex engine and replace it with an alternate pattern-matching library.
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Table 5-18. Alternate regex engines
re::engine::RE2 - Russ Cox’s RE2 regex engine
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One engine of special note is Russ Cox’s RE2 library. It’s a C and C++ library that’s used in the Go programming language, among many other places. The interesting thing is that it maintains a high level Perl compatibility, including good UTF-8 support, while avoiding the potential pitfalls of catastrophic backtracking. It does this because unlike Perl, whose engine is a recursive backtracker, RE2 uses a hybrid NFA/DFA approach that never gets bogged down in pathological cases.
This can be critical in time-sensitive applications where you want to let users provide their own pattern, but you cannot risk letting their search take forever. First written for Google’s Code Search, where time is of the essence, RE2 is also used via its Perl interface at http://grep.cpan.me. This site lets you enter a search pattern that runs over everything in CPAN.
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You have to eliminate even harsher. Prime factoring is also expressible in Perl regular expression.