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1 .TH PCREMATCHING 3
2 .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 them, whereas the alternative algorithm finds all three.
30 .
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 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 .
41 .SH "THE STANDARD MATCHING ALGORITHM"
42 .rs
43 .sp
44 In the terminology of Jeffrey Friedl's book "Mastering Regular
45 Expressions", 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 .
66 .SH "THE ALTERNATIVE MATCHING ALGORITHM"
67 .rs
68 .sp
69 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 .P
77 Although the general principle of this matching algorithm is that it scans the
78 subject string only once, without backtracking, there is one exception: when a
79 lookaround assertion is encountered, the characters following or preceding the
80 current point have to be independently inspected.
81 .P
82 The scan continues until either the end of the subject is reached, or there are
83 no more unterminated paths. At this point, terminated paths represent the
84 different matching possibilities (if there are none, the match has failed).
85 Thus, if there is more than one possible match, this algorithm finds all of
86 them, and in particular, it finds the longest. The matches are returned in
87 decreasing order of length. There is an option to stop the algorithm after the
88 first match (which is necessarily the shortest) is found.
89 .P
90 Note that all the matches that are found start at the same point in the
91 subject. If the pattern
92 .sp
93 cat(er(pillar)?)?
94 .sp
95 is matched against the string "the caterpillar catchment", the result will be
96 the three strings "caterpillar", "cater", and "cat" that start at the fifth
97 character of the subject. The algorithm does not automatically move on to find
98 matches that start at later positions.
99 .P
100 There are a number of features of PCRE regular expressions that are not
101 supported by the alternative matching algorithm. They are as follows:
102 .P
103 1. Because the algorithm finds all possible matches, the greedy or ungreedy
104 nature of repetition quantifiers is not relevant. Greedy and ungreedy
105 quantifiers are treated in exactly the same way. However, possessive
106 quantifiers can make a difference when what follows could also match what is
107 quantified, for example in a pattern like this:
108 .sp
109 ^a++\ew!
110 .sp
111 This pattern matches "aaab!" but not "aaa!", which would be matched by a
112 non-possessive quantifier. Similarly, if an atomic group is present, it is
113 matched as if it were a standalone pattern at the current point, and the
114 longest match is then "locked in" for the rest of the overall pattern.
115 .P
116 2. When dealing with multiple paths through the tree simultaneously, it is not
117 straightforward to keep track of captured substrings for the different matching
118 possibilities, and PCRE's implementation of this algorithm does not attempt to
119 do this. This means that no captured substrings are available.
120 .P
121 3. Because no substrings are captured, back references within the pattern are
122 not supported, and cause errors if encountered.
123 .P
124 4. For the same reason, conditional expressions that use a backreference as the
125 condition or test for a specific group recursion are not supported.
126 .P
127 5. Because many paths through the tree may be active, the \eK escape sequence,
128 which resets the start of the match when encountered (but may be on some paths
129 and not on others), is not supported. It causes an error if encountered.
130 .P
131 6. Callouts are supported, but the value of the \fIcapture_top\fP field is
132 always 1, and the value of the \fIcapture_last\fP field is always -1.
133 .P
134 7. The \eC escape sequence, which (in the standard algorithm) matches a single
135 byte, even in UTF-8 mode, is not supported because the alternative algorithm
136 moves through the subject string one character at a time, for all active paths
137 through the tree.
138 .P
139 8. Except for (*FAIL), the backtracking control verbs such as (*PRUNE) are not
140 supported. (*FAIL) is supported, and behaves like a failing negative assertion.
141 .
142 .SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"
143 .rs
144 .sp
145 Using the alternative matching algorithm provides the following advantages:
146 .P
147 1. All possible matches (at a single point in the subject) are automatically
148 found, and in particular, the longest match is found. To find more than one
149 match using the standard algorithm, you have to do kludgy things with
150 callouts.
151 .P
152 2. Because the alternative algorithm scans the subject string just once, and
153 never needs to backtrack, it is possible to pass very long subject strings to
154 the matching function in several pieces, checking for partial matching each
155 time. Although it is possible to do multi-segment matching using the standard
156 algorithm (\fBpcre_exec()\fP), by retaining partially matched substrings, it is
157 more complicated. The
158 .\" HREF
159 \fBpcrepartial\fP
160 .\"
161 documentation gives details of partial matching and discusses multi-segment
162 matching.
163 .
164 .
165 .SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"
166 .rs
167 .sp
168 The alternative algorithm suffers from a number of disadvantages:
169 .P
170 1. It is substantially slower than the standard algorithm. This is partly
171 because it has to search for all possible matches, but is also because it is
172 less susceptible to optimization.
173 .P
174 2. Capturing parentheses and back references are not supported.
175 .P
176 3. Although atomic groups are supported, their use does not provide the
177 performance advantage that it does for the standard algorithm.
178 .
179 .
180 .SH AUTHOR
181 .rs
182 .sp
183 .nf
184 Philip Hazel
185 University Computing Service
186 Cambridge CB2 3QH, England.
187 .fi
188 .
189 .
190 .SH REVISION
191 .rs
192 .sp
193 .nf
194 Last updated: 17 November 2010
195 Copyright (c) 1997-2010 University of Cambridge.
196 .fi

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