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3 PCRE - Perl-compatible regular expressions
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
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26 <something> <something else> <something further>
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28 there are three possible answers. The standard algorithm finds only one of
29 them, whereas the DFA algorithm finds all three.
30 .
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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 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 .
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44 In the terminology of Jeffrey Friedl's book \fIMastering Regular
45 Expressions\fP, the standard algorithm is an "NFA algorithm". It conducts a
46 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 .
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69 DFA stands for "deterministic finite automaton", but you do not need to
70 understand the origins of that name. This algorithm conducts a breadth-first
71 search of the tree. Starting from the first matching point in the subject, it
72 scans the subject string from left to right, once, character by character, and
73 as it does this, it remembers all the paths through the tree that represent
74 valid matches.
75 .P
76 The scan continues until either the end of the subject is reached, or there are
77 no more unterminated paths. At this point, terminated paths represent the
78 different matching possibilities (if there are none, the match has failed).
79 Thus, if there is more than one possible match, this algorithm finds all of
80 them, and in particular, it finds the longest. In PCRE, there is an option to
81 stop the algorithm after the first match (which is necessarily the shortest)
82 has been found.
83 .P
84 Note that all the matches that are found start at the same point in the
85 subject. If the pattern
86 .sp
87 cat(er(pillar)?)
88 .sp
89 is matched against the string "the caterpillar catchment", the result will be
90 the three strings "cat", "cater", and "caterpillar" that start at the fourth
91 character of the subject. The algorithm does not automatically move on to find
92 matches that start at later positions.
93 .P
94 There are a number of features of PCRE regular expressions that are not
95 supported by the DFA matching algorithm. They are as follows:
96 .P
97 1. Because the algorithm finds all possible matches, the greedy or ungreedy
98 nature of repetition quantifiers is not relevant. Greedy and ungreedy
99 quantifiers are treated in exactly the same way.
100 .P
101 2. When dealing with multiple paths through the tree simultaneously, it is not
102 straightforward to keep track of captured substrings for the different matching
103 possibilities, and PCRE's implementation of this algorithm does not attempt to
104 do this. This means that no captured substrings are available.
105 .P
106 3. Because no substrings are captured, back references within the pattern are
107 not supported, and cause errors if encountered.
108 .P
109 4. For the same reason, conditional expressions that use a backreference as the
110 condition are not supported.
111 .P
112 5. Callouts are supported, but the value of the \fIcapture_top\fP field is
113 always 1, and the value of the \fIcapture_last\fP field is always -1.
114 .P
115 6.
116 The \eC escape sequence, which (in the standard algorithm) matches a single
117 byte, even in UTF-8 mode, is not supported because the DFA algorithm moves
118 through the subject string one character at a time, for all active paths
119 through the tree.
120 .
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124 Using the DFA matching algorithm provides the following advantages:
125 .P
126 1. All possible matches (at a single point in the subject) are automatically
127 found, and in particular, the longest match is found. To find more than one
128 match using the standard algorithm, you have to do kludgy things with
129 callouts.
130 .P
131 2. There is much better support for partial matching. The restrictions on the
132 content of the pattern that apply when using the standard algorithm for partial
133 matching do not apply to the DFA algorithm. For non-anchored patterns, the
134 starting position of a partial match is available.
135 .P
136 3. Because the DFA algorithm scans the subject string just once, and never
137 needs to backtrack, it is possible to pass very long subject strings to the
138 matching function in several pieces, checking for partial matching each time.
139 .
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143 The DFA algorithm suffers from a number of disadvantages:
144 .P
145 1. It is substantially slower than the standard algorithm. This is partly
146 because it has to search for all possible matches, but is also because it is
147 less susceptible to optimization.
148 .P
149 2. Capturing parentheses and back references are not supported.
150 .P
151 3. The "atomic group" feature of PCRE regular expressions is supported, but
152 does not provide the advantage that it does for the standard algorithm.
153 .P
154 .in 0
155 Last updated: 06 June 2006
156 .br
157 Copyright (c) 1997-2006 University of Cambridge.

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