These regexes are much more powerful than regular expressions, in fact they can do things that even Typ-1 langauges (context-free languages) can't. I've not yet seen a proof that they are Turing complete, so I don't know if they are.
In a sense they're ‘obviously’ Turing-complete, since they can contain embedded Perl code; but I assume that's not what you meant. What's another example of Perl regexes recognising a language that a CFG can't? (It sounds vaguely like a challenge, but I'm just politely curious.)
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