Below is some analysis of use of backreferences in Perl, done by
Eric Niebler <ericne#micorosft.com> for the C++ committee.
This post is stolen from the library subgroup committee reflector.
The C++ committee is looking at which kind of regular expresssions
to provide as standard in the C++ Standard Library. Thought I'd post
it here in case it's useful to the Ocaml team which is also looking
at RE libraries.

------------------------------------------------------------------------

OK, I have some numbers.  As a refresher, POSIX-extended doesn't do
backreferences, but guarantees complexity O(SN) where S is the number of
states in the NFA, and N is the number of characters in the input
string.  ECMAScript does backreferences, but worst-case complexity is
O(2^N).

For a language where backreferences are available, I thought it would be
interesting to see how often people make use of this feature.  So I
downloaded the CPAN archive and analyzed the perl scripts there.  Here
is what I found:

     - I found 165228 perl scripts/modules in CPAN [1].
     - Of those, 68501 use regular expressions [2].
     - Of those, 32359 (or 47 percent) use backreferences [3].

So, nearly half of all perl scripts on CPAN that use regular expressions
make use of the backreference feature.  IMO this argues strongly in
favor of supporting backreferences in C++.  (Backreferences can only be
handled by a backtracking NFA engine, IIRC.)

There are other features besides backreferences that can only be
provided by a backtracking NFA.  These features include non-greedy
quantification, positive and negative look-ahead and look-behind
assertions, independent sub-expressions, conditional sub-expressions,
and backreferences within the pattern itself.  I did a separate analysis
to see how often these features were used.  Here's what I found:

     - Of the 68501 scripts that use regular expressions, 12199 (or 18
percent) use at least one of the features listed above [4].

If I count the files that use either backreferences or one of these
other features, I find that:

     - 33881 files, or 49.5 percent, use some feature that requires a
backtracking NFA engine.

To get some idea of how many false-positives were turning up in my
tests, I ran the same search against the files which do not use regular
expressions at all.  I found that of the 96727 scripts that do *not* use
regular expressions [2], 2300 tested positive for a backtracking regex
feature.  That amounts to a 2% false positive rate.  So it would be fair
to knock 2% off the percentages quoted above.

Eric



[1] - I was only looking at files with .pm and .pl extensions, after
extracting all archives with .tar.gz, .tgz, and .zip extensions.
[2] - A perl file was determined to use regular expressions if it
matched the pattern, "[=!]~ *[^ty ]".  That is, if it used the operators
=~ or !~ for matching or substituting (i.e. not character translation).
[3] - A file was determined to use backreferences if it contained the
pattern, "\$[1-9][^0-9]".
[4] - A file was included in this total if it matched one of the
following patterns:
         \(\?=                      // a positive look-ahead assertion
         \(\?!                      // a negative look-ahead assertion
         [0-9]\}\?                  // a non-greedy quantifier
         [+*]\?                     // also a non-greedy quantifier
         \(\?> // an independent sub-expression
         \(\?<=                     // a positive look-behind assertion
         \(\?<!                     // a negative look-behind assertion
         \(\?\(                     // a conditional sub-expression
         [=!]~.*\\[1-9][^0-9]       // a backreference used within a
pattern



-- 
John Max Skaller, mailto:skaller@ozemail.com.au
snail:10/1 Toxteth Rd, Glebe, NSW 2037, Australia.
voice:61-2-9660-0850


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