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1 nigel 79 .TH PCREMATCHING 3
2 nigel 77 .SH NAME
3     PCRE - Perl-compatible regular expressions
4     .SH "PCRE MATCHING ALGORITHMS"
5     .rs
6     .sp
7     This document describes the two different algorithms that are available in PCRE
8     for matching a compiled regular expression against a given subject string. The
9     "standard" algorithm is the one provided by the \fBpcre_exec()\fP function.
10     This works in the same was as Perl's matching function, and provides a
11     Perl-compatible matching operation.
12     .P
13     An alternative algorithm is provided by the \fBpcre_dfa_exec()\fP function;
14     this operates in a different way, and is not Perl-compatible. It has advantages
15     and disadvantages compared with the standard algorithm, and these are described
16     below.
17     .P
18     When there is only one possible way in which a given subject string can match a
19     pattern, the two algorithms give the same answer. A difference arises, however,
20     when there are multiple possibilities. For example, if the pattern
21     .sp
22     ^<.*>
23     .sp
24     is matched against the string
25     .sp
26     <something> <something else> <something further>
27     .sp
28     there are three possible answers. The standard algorithm finds only one of
29 nigel 93 them, whereas the alternative algorithm finds all three.
30 nigel 77 .
31     .SH "REGULAR EXPRESSIONS AS TREES"
32     .rs
33     .sp
34     The set of strings that are matched by a regular expression can be represented
35     as a tree structure. An unlimited repetition in the pattern makes the tree of
36     infinite size, but it is still a tree. Matching the pattern to a given subject
37     string (from a given starting point) can be thought of as a search of the tree.
38 nigel 91 There are two ways to search a tree: depth-first and breadth-first, and these
39     correspond to the two matching algorithms provided by PCRE.
40 nigel 77 .
41     .SH "THE STANDARD MATCHING ALGORITHM"
42     .rs
43     .sp
44 ph10 148 In the terminology of Jeffrey Friedl's book "Mastering Regular
45     Expressions", the standard algorithm is an "NFA algorithm". It conducts a
46 nigel 77 depth-first search of the pattern tree. That is, it proceeds along a single
47     path through the tree, checking that the subject matches what is required. When
48     there is a mismatch, the algorithm tries any alternatives at the current point,
49     and if they all fail, it backs up to the previous branch point in the tree, and
50     tries the next alternative branch at that level. This often involves backing up
51     (moving to the left) in the subject string as well. The order in which
52     repetition branches are tried is controlled by the greedy or ungreedy nature of
53     the quantifier.
54     .P
55     If a leaf node is reached, a matching string has been found, and at that point
56     the algorithm stops. Thus, if there is more than one possible match, this
57     algorithm returns the first one that it finds. Whether this is the shortest,
58     the longest, or some intermediate length depends on the way the greedy and
59     ungreedy repetition quantifiers are specified in the pattern.
60     .P
61     Because it ends up with a single path through the tree, it is relatively
62     straightforward for this algorithm to keep track of the substrings that are
63     matched by portions of the pattern in parentheses. This provides support for
64     capturing parentheses and back references.
65     .
66 nigel 93 .SH "THE ALTERNATIVE MATCHING ALGORITHM"
67 nigel 77 .rs
68     .sp
69 nigel 93 This algorithm conducts a breadth-first search of the tree. Starting from the
70     first matching point in the subject, it scans the subject string from left to
71     right, once, character by character, and as it does this, it remembers all the
72     paths through the tree that represent valid matches. In Friedl's terminology,
73     this is a kind of "DFA algorithm", though it is not implemented as a
74     traditional finite state machine (it keeps multiple states active
75     simultaneously).
76 nigel 77 .P
77     The scan continues until either the end of the subject is reached, or there are
78     no more unterminated paths. At this point, terminated paths represent the
79     different matching possibilities (if there are none, the match has failed).
80     Thus, if there is more than one possible match, this algorithm finds all of
81     them, and in particular, it finds the longest. In PCRE, there is an option to
82     stop the algorithm after the first match (which is necessarily the shortest)
83     has been found.
84     .P
85     Note that all the matches that are found start at the same point in the
86     subject. If the pattern
87     .sp
88     cat(er(pillar)?)
89     .sp
90     is matched against the string "the caterpillar catchment", the result will be
91     the three strings "cat", "cater", and "caterpillar" that start at the fourth
92     character of the subject. The algorithm does not automatically move on to find
93     matches that start at later positions.
94     .P
95     There are a number of features of PCRE regular expressions that are not
96 nigel 93 supported by the alternative matching algorithm. They are as follows:
97 nigel 77 .P
98     1. Because the algorithm finds all possible matches, the greedy or ungreedy
99     nature of repetition quantifiers is not relevant. Greedy and ungreedy
100 nigel 93 quantifiers are treated in exactly the same way. However, possessive
101     quantifiers can make a difference when what follows could also match what is
102     quantified, for example in a pattern like this:
103     .sp
104     ^a++\ew!
105     .sp
106     This pattern matches "aaab!" but not "aaa!", which would be matched by a
107     non-possessive quantifier. Similarly, if an atomic group is present, it is
108     matched as if it were a standalone pattern at the current point, and the
109     longest match is then "locked in" for the rest of the overall pattern.
110 nigel 77 .P
111     2. When dealing with multiple paths through the tree simultaneously, it is not
112     straightforward to keep track of captured substrings for the different matching
113     possibilities, and PCRE's implementation of this algorithm does not attempt to
114     do this. This means that no captured substrings are available.
115     .P
116     3. Because no substrings are captured, back references within the pattern are
117     not supported, and cause errors if encountered.
118     .P
119     4. For the same reason, conditional expressions that use a backreference as the
120 nigel 93 condition or test for a specific group recursion are not supported.
121 nigel 77 .P
122     5. Callouts are supported, but the value of the \fIcapture_top\fP field is
123     always 1, and the value of the \fIcapture_last\fP field is always -1.
124     .P
125     6.
126     The \eC escape sequence, which (in the standard algorithm) matches a single
127 nigel 93 byte, even in UTF-8 mode, is not supported because the alternative algorithm
128     moves through the subject string one character at a time, for all active paths
129 nigel 77 through the tree.
130     .
131 nigel 93 .SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"
132 nigel 77 .rs
133     .sp
134 nigel 93 Using the alternative matching algorithm provides the following advantages:
135 nigel 77 .P
136     1. All possible matches (at a single point in the subject) are automatically
137     found, and in particular, the longest match is found. To find more than one
138     match using the standard algorithm, you have to do kludgy things with
139     callouts.
140     .P
141     2. There is much better support for partial matching. The restrictions on the
142     content of the pattern that apply when using the standard algorithm for partial
143 nigel 93 matching do not apply to the alternative algorithm. For non-anchored patterns,
144     the starting position of a partial match is available.
145 nigel 77 .P
146 nigel 93 3. Because the alternative algorithm scans the subject string just once, and
147     never needs to backtrack, it is possible to pass very long subject strings to
148     the matching function in several pieces, checking for partial matching each
149     time.
150 nigel 77 .
151 nigel 93 .SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"
152 nigel 77 .rs
153     .sp
154 nigel 93 The alternative algorithm suffers from a number of disadvantages:
155 nigel 77 .P
156     1. It is substantially slower than the standard algorithm. This is partly
157     because it has to search for all possible matches, but is also because it is
158     less susceptible to optimization.
159     .P
160     2. Capturing parentheses and back references are not supported.
161     .P
162 nigel 93 3. Although atomic groups are supported, their use does not provide the
163     performance advantage that it does for the standard algorithm.
164 ph10 99 .
165     .
166     .SH AUTHOR
167     .rs
168     .sp
169     .nf
170     Philip Hazel
171     University Computing Service
172     Cambridge CB2 3QH, England.
173     .fi
174     .
175     .
176     .SH REVISION
177     .rs
178     .sp
179     .nf
180     Last updated: 06 March 2007
181     Copyright (c) 1997-2007 University of Cambridge.
182     .fi

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