First of all sorry for getting the numbering wrong, I misremembered REG as being Typ-0 and Turing as being Typ-3, it's the other way round.

What's another example of Perl regexes recognising a language that a CFG can't?
m/^(\w+)\1$/

Is already outside CFG.

CFG is parsed by a non-deterministic finite automaton which has access to a stack of infinite size.

Since it can only access the top element of the stack, it has only access to the capture in reverse order, or with a finite look-behind on the stack (implemented by storing some values in the state of the NFA). A more formal proof can be made with the Pumping lemma for context-free languages.

I also think that the regex primality test is outside of CFG, but I've never proven that, so don't rely on it ;-)

In reply to Re^4: check for square-number with a regex by moritz
in thread check for square-number with a regex by Ratazong

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