NAME
PCRE - Perl-compatible regular expressions
PCRE MATCHING ALGORITHMS
This document describes the two different algorithms that are available
in PCRE for matching a compiled regular expression against a given
subject 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
represented 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
Expressions", 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
alternatives 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
that point the algorithm stops. Thus, if there is more than one
possible match, this algorithm returns the first one that it finds.
Whether this is the shortest, the longest, or some intermediate length
depends on the way the greedy and ungreedy repetition quantifiers are
specified in the pattern.
Because it ends up with a single path through the tree, it is
relatively straightforward for this algorithm to keep track of the
substrings that are matched by portions of the pattern in parentheses.
This provides support for capturing parentheses and back references.
THE ALTERNATIVE MATCHING ALGORITHM
This algorithm conducts a breadth-first search of the tree. Starting
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).
Although the general principle of this matching algorithm is that it
scans the subject string only once, without backtracking, there is one
exception: when a lookaround assertion is encountered, the characters
following or preceding the current point have to be independently
inspected.
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. There is an option to stop the algorithm after the first match
(which is necessarily the shortest) is 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
automatically 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,
possessive 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
substrings are available.
3. Because no substrings are captured, back references within the
pattern are not supported, and cause errors if encountered.
4. For the same reason, conditional expressions that use a
backreference as the condition or test for a specific group recursion
are not supported.
5. Because many paths through the tree may be active, the \K escape
sequence, which resets the start of the match when encountered (but may
be on some paths and not on others), is not supported. It causes an
error if encountered.
6. Callouts are supported, but the value of the capture_top field is
always 1, and the value of the capture_last field is always -1.
7. The \C escape sequence, which (in the standard algorithm) matches a
single byte, even in UTF-8 mode, is not supported because the
alternative algorithm moves through the subject string one character at
a 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
advantages:
1. All possible matches (at a single point in the subject) are
automatically 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. 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. The pcrepartial documentation gives
details of partial matching.
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: 29 September 2009
Copyright (c) 1997-2009 University of Cambridge.