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Re^3: check for power of a number with regex

by blokhead (Monsignor)
on Oct 26, 2009 at 13:37 UTC ( #803258=note: print w/replies, xml ) Need Help??

in reply to Re^2: check for power of a number with regex
in thread check for power of a number with regex

Any context-free language over a single-character alphabet is also regular (which can be shown using, for example, Parikh's theorem). So since this "language of exponentials" is non-regular, it is also non-context-free. Another way to look at it is that the pumping lemma for CFLs essentially collapses into the pumping lemma for regular languages when applied to single-character alphabets, because the concatenation operator is commutative on strings over a single-character alphabet.

I do stand by my intuition that backrefs alone (i.e., classical regexes + backrefs) won't help. But you are right, I am not able to prove it -- there is just no formal model that I'm aware of that exactly captures the expressivity of those operations, that would be amenable to impossibility proofs. I admit I hadn't thought of the new named captures & rules from 5.10 (I'm a bit behind the times). Clearly the named captures alone won't get you the regex desired in this case, but maybe some clever combination of both named rules & backrefs? I remain slightly skeptical but open-minded ;)


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