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pcrematching
PCRE MATCHING ALGORITHMS
This document describes the two different algorithms that are available
in PCRE for matching a compiled regular expression against a given sub-
ject string. The "standard" algorithm is the one provided by the
pcre_exec() function. This works in the same was as Perl's matching
function, and provides a Perl-compatible matching operation.
An alternative algorithm is provided by the pcre_dfa_exec() function;
this operates in a different way, and is not Perl-compatible. It has
advantages and disadvantages compared with the standard algorithm, and
these are described below.
When there is only one possible way in which a given subject string can
match a pattern, the two algorithms give the same answer. A difference
arises, however, when there are multiple possibilities. For example, if
the pattern
^<.*>
is matched against the string
<something> <something else> <something further>
there are three possible answers. The standard algorithm finds only one
of them, whereas the alternative algorithm finds all three.
REGULAR EXPRESSIONS AS TREES
The set of strings that are matched by a regular expression can be rep-
resented as a tree structure. An unlimited repetition in the pattern
makes the tree of infinite size, but it is still a tree. Matching the
pattern to a given subject string (from a given starting point) can be
thought of as a search of the tree. There are two ways to search a
tree: depth-first and breadth-first, and these correspond to the two
matching algorithms provided by PCRE.
THE STANDARD MATCHING ALGORITHM
In the terminology of Jeffrey Friedl's book "Mastering Regular Expres-
sions", the standard algorithm is an "NFA algorithm". It conducts a
depth-first search of the pattern tree. That is, it proceeds along a
single path through the tree, checking that the subject matches what is
required. When there is a mismatch, the algorithm tries any alterna-
tives at the current point, and if they all fail, it backs up to the
previous branch point in the tree, and tries the next alternative
branch at that level. This often involves backing up (moving to the
left) in the subject string as well. The order in which repetition
branches are tried is controlled by the greedy or ungreedy nature of
the quantifier.
If a leaf node is reached, a matching string has been found, and at
from the first matching point in the subject, it scans the subject
string from left to right, once, character by character, and as it does
this, it remembers all the paths through the tree that represent valid
matches. In Friedl's terminology, this is a kind of "DFA algorithm",
though it is not implemented as a traditional finite state machine (it
keeps multiple states active simultaneously).
The scan continues until either the end of the subject is reached, or
there are no more unterminated paths. At this point, terminated paths
represent the different matching possibilities (if there are none, the
match has failed). Thus, if there is more than one possible match,
this algorithm finds all of them, and in particular, it finds the
longest. In PCRE, there is an option to stop the algorithm after the
first match (which is necessarily the shortest) has been found.
Note that all the matches that are found start at the same point in the
subject. If the pattern
cat(er(pillar)?)
is matched against the string "the caterpillar catchment", the result
will be the three strings "cat", "cater", and "caterpillar" that start
at the fourth character of the subject. The algorithm does not automat-
ically move on to find matches that start at later positions.
There are a number of features of PCRE regular expressions that are not
supported by the alternative matching algorithm. They are as follows:
1. Because the algorithm finds all possible matches, the greedy or
ungreedy nature of repetition quantifiers is not relevant. Greedy and
ungreedy quantifiers are treated in exactly the same way. However, pos-
sessive quantifiers can make a difference when what follows could also
match what is quantified, for example in a pattern like this:
^a++\w!
This pattern matches "aaab!" but not "aaa!", which would be matched by
a non-possessive quantifier. Similarly, if an atomic group is present,
it is matched as if it were a standalone pattern at the current point,
and the longest match is then "locked in" for the rest of the overall
pattern.
2. When dealing with multiple paths through the tree simultaneously, it
is not straightforward to keep track of captured substrings for the
different matching possibilities, and PCRE's implementation of this
algorithm does not attempt to do this. This means that no captured sub-
strings are available.
3. Because no substrings are captured, back references within the pat-
tern are not supported, and cause errors if encountered.
4. For the same reason, conditional expressions that use a backrefer-
time, for all active paths through the tree.
8. Except for (*FAIL), the backtracking control verbs such as (*PRUNE)
are not supported. (*FAIL) is supported, and behaves like a failing
negative assertion.
ADVANTAGES OF THE ALTERNATIVE ALGORITHM
Using the alternative matching algorithm provides the following advan-
tages:
1. All possible matches (at a single point in the subject) are automat-
ically found, and in particular, the longest match is found. To find
more than one match using the standard algorithm, you have to do kludgy
things with callouts.
2. There is much better support for partial matching. The restrictions
on the content of the pattern that apply when using the standard algo-
rithm for partial matching do not apply to the alternative algorithm.
For non-anchored patterns, the starting position of a partial match is
available.
3. Because the alternative algorithm scans the subject string just
once, and never needs to backtrack, it is possible to pass very long
subject strings to the matching function in several pieces, checking
for partial matching each time.
DISADVANTAGES OF THE ALTERNATIVE ALGORITHM
The alternative algorithm suffers from a number of disadvantages:
1. It is substantially slower than the standard algorithm. This is
partly because it has to search for all possible matches, but is also
because it is less susceptible to optimization.
2. Capturing parentheses and back references are not supported.
3. Although atomic groups are supported, their use does not provide the
performance advantage that it does for the standard algorithm.
AUTHOR
Philip Hazel
University Computing Service
Cambridge CB2 3QH, England.
REVISION
Last updated: 19 April 2008
Copyright (c) 1997-2008 University of Cambridge.