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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 documentation 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 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.
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 PCRE2.
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
backreferences.
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.
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 is 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.
PCRE2'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 PCRE2_NO_AUTO_POSSESS option when compiling.
There are a number of features of PCRE2 regular expressions that are not supported or
behave differently in the alternative matching function. Those that are not supported
cause an error if encountered.
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 substrings are available.
3. Because no substrings are captured, backreferences within the pattern are not
supported.
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. Again for the same reason, script runs are not supported.
6. 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.
7. 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.
8. 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 subject string one character (not code unit) at a time, for
all active paths through the tree.
9. Except for (*FAIL), the backtracking control verbs such as (*PRUNE) are not supported.
(*FAIL) is supported, and behaves like a failing negative assertion.
10. The PCRE2_MATCH_INVALID_UTF option for pcre2_compile() is not supported by
pcre2_dfa_match().
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 (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 also possible to do multi-segment matching using the standard algorithm, by
retaining partially matched substrings, it is more complicated. 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, backreferences, script runs, and matching within invalid UTF
string 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: 23 May 2019
Copyright (c) 1997-2019 University of Cambridge.