I (and others in this thread) explicitely mentioned no using (?{}) and (??{}). Allowing those means you have the full power of Perl available. It would mean that anything you can do in Perl, you can to with a "regular expression", and the question "can I do foo with a regular expression" becomes a non-question.

And I would have used (?{}) differently anyway. Something like:

/^(a+)(b+)(c+)$(?(?{length($1) == length($2) && length($2) == length($
+3)})|(*FAIL))/;
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But that's just a fancy way of writing:

/^(a+)(b+)(c+)$/ && length($1) == length($2) && length($2) == length($
+3);
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And you can solve the "match a square" with:

/^([0-9]+)$(?(?{sqrt($1) == int sqrt($1)})|(*FAIL))/;
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Or in general, match "whatever" by:

/^(.*)$(?(?{is_whatever($1)})|(*FAIL))/;
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after writing the appropriate "is_whatever" function.

But that means the question no longer is "how can I do foo with a regexp", but "how can I do foo in Perl".