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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 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 DFA 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 standard 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
that point the algorithm stops. Thus, if there is more than one possi‐
ble 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 rela‐
tively straightforward for this algorithm to keep track of the sub‐
strings that are matched by portions of the pattern in parentheses.
This provides support for capturing parentheses and back references.
THE DFA MATCHING ALGORITHM
DFA stands for "deterministic finite automaton", but you do not need to
understand the origins of that name. 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, charac‐
ter by character, and as it does this, it remembers all the paths
through the tree that represent valid matches.
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 long‐
est. 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 DFA 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.
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‐
ence as the condition are not supported.
5. 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.
6. The \C escape sequence, which (in the standard algorithm) matches a
single byte, even in UTF-8 mode, is not supported because the DFA algo‐
rithm moves through the subject string one character at a time, for all
active paths through the tree.
ADVANTAGES OF THE DFA ALGORITHM
Using the DFA matching algorithm provides the following advantages:
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 DFA algorithm. For non-
anchored patterns, the starting position of a partial match is avail‐
able.
3. Because the DFA 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 par‐
tial matching each time.
DISADVANTAGES OF THE DFA ALGORITHM
The DFA 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. The "atomic group" feature of PCRE regular expressions is supported,
but does not provide the advantage that it does for the standard algo‐
rithm.
Last updated: 28 February 2005Copyright (c) 1997-2005 University of Cambridge.
PCREMATCHING(3)
