PCREMATCHING(3) Library Functions Manual PCREMATCHING(3)
PCRE - Perl-compatible regular expressions
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(), pcre16_exec() and pcre32_exec()
functions. These work 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 pcrejit
documentation is compatible with these functions.
An alternative algorithm is provided by the pcre_dfa_exec(),
pcre16_dfa_exec() and pcre32_dfa_exec() functions; they operate
in a different way, and are not Perl-compatible. This alternative
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.
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.
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.
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. The matches are returned
in decreasing order of length. 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 "caterpillar", "cater", and
"cat" that start at the fifth character of the subject. The
algorithm does not automatically move on to find matches that
start at later positions.
PCRE's "auto-possessification" optimization usually applies to
character repeats at the end of a pattern (as well as
internally). For example, 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 PCRE_NO_AUTO_POSSESS option
when compiling.
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)
always matches a single data unit, even in UTF-8, UTF-16 or
UTF-32 modes, is not supported in these modes, because the
alternative algorithm moves through the subject string one
character (not data 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.
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 (except for lookbehinds),
it is possible to pass very long subject strings to the matching
function in several pieces, checking for partial matching each
time. Although it is possible to do multi-segment matching using
the standard algorithm by retaining partially matched substrings,
it is more complicated. The pcrepartial documentation gives
details of partial matching and discusses multi-segment matching.
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.
Philip Hazel
University Computing Service
Cambridge CB2 3QH, England.
Last updated: 12 November 2013
Copyright (c) 1997-2012 University of Cambridge.
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PCRE 8.34 12 November 2013 PCREMATCHING(3)
Pages that refer to this page: pcretest(1), pcreapi(3), pcrepattern(3), pcresyntax(3)
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