PCRE2MATCHING(3)PCRE2MATCHING(3)NAME
PCRE2 - Perl-compatible regular expressions (revised API)
PCRE2 MATCHING ALGORITHMS
This document describes the two different algorithms that are available
in PCRE2 for matching a compiled regular expression against a given
subject string. The "standard" algorithm is the one provided by the
pcre2_match() function. This works in the same as as Perl's matching
function, and provide a Perl-compatible matching operation. The just-
in-time (JIT) optimization that is described in the pcre2jit documenta‐
tion is compatible with this function.
An alternative algorithm is provided by the pcre2_dfa_match() function;
it operates in a different way, and is not Perl-compatible. This alter‐
native 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 PCRE2.
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 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 long‐
est. The matches are returned in decreasing order of length. There is
an option to stop the algorithm after the first match (which is neces‐
sarily 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
is the three strings "caterpillar", "cater", and "cat" that start at
the fifth character of the subject. The algorithm does not automati‐
cally move on to find matches that start at later positions.
PCRE2's "auto-possessification" optimization usually applies to charac‐
ter repeats at the end of a pattern (as well as internally). For exam‐
ple, the pattern "a\d+" is compiled as if it were "a\d++" because there
is no point even considering the possibility of backtracking into the
repeated digits. For DFA matching, this means that only one possible
match is found. If you really do want multiple matches in such cases,
either use an ungreedy repeat ("a\d+?") or set the PCRE2_NO_AUTO_POS‐
SESS option when compiling.
There are a number of features of PCRE2 regular expressions that are
not supported by the alternative matching algorithm. They are as fol‐
lows:
1. Because the algorithm finds all possible matches, the greedy or
ungreedy nature of repetition quantifiers is not relevant (though it
may affect auto-possessification, as just described). During matching,
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 PCRE2'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 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 0.
7. The \C escape sequence, which (in the standard algorithm) always
matches a single code unit, even in a UTF mode, is not supported in
these modes, because the alternative algorithm moves through the sub‐
ject string one character (not code unit) 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 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. Because the alternative algorithm scans the subject string just
once, and never needs to backtrack (except for lookbehinds), it is pos‐
sible to pass very long subject strings to the matching function in
several pieces, checking for partial matching each time. Although it is
also possible to do multi-segment matching using the standard algo‐
rithm, by retaining partially matched substrings, it is more compli‐
cated. The pcre2partial documentation gives details of partial matching
and discusses multi-segment 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, England.
REVISION
Last updated: 29 September 2014
Copyright (c) 1997-2014 University of Cambridge.
PCRE2 10.00 29 September 2014 PCRE2MATCHING(3)
