PCREMATCHING(3) Introduction to Library Functions PCREMATCHING(3)

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(), 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.

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. 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.

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 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.

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: 12 November 2013
Copyright (c) 1997-2012 University of Cambridge.

PCRE 8.34 12 November 2013 PCREMATCHING(3)