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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 and
10 \fBpcre16_exec()\fP functions. These work in the same was as Perl's matching
11 function, and provide a Perl-compatible matching operation. The just-in-time
12 (JIT) optimization that is described in the
13 .\" HREF
14 \fBpcrejit\fP
15 .\"
16 documentation is compatible with these functions.
17 .P
18 An alternative algorithm is provided by the \fBpcre_dfa_exec()\fP and
19 \fBpcre16_dfa_exec()\fP functions; they operate in a different way, and are not
20 Perl-compatible. This alternative has advantages and disadvantages compared
21 with the standard algorithm, and these are described below.
22 .P
23 When there is only one possible way in which a given subject string can match a
24 pattern, the two algorithms give the same answer. A difference arises, however,
25 when there are multiple possibilities. For example, if the pattern
26 .sp
27 ^<.*>
28 .sp
29 is matched against the string
30 .sp
31 <something> <something else> <something further>
32 .sp
33 there are three possible answers. The standard algorithm finds only one of
34 them, whereas the alternative algorithm finds all three.
35 .
36 .
37 .SH "REGULAR EXPRESSIONS AS TREES"
38 .rs
39 .sp
40 The set of strings that are matched by a regular expression can be represented
41 as a tree structure. An unlimited repetition in the pattern makes the tree of
42 infinite size, but it is still a tree. Matching the pattern to a given subject
43 string (from a given starting point) can be thought of as a search of the tree.
44 There are two ways to search a tree: depth-first and breadth-first, and these
45 correspond to the two matching algorithms provided by PCRE.
46 .
47 .
48 .SH "THE STANDARD MATCHING ALGORITHM"
49 .rs
50 .sp
51 In the terminology of Jeffrey Friedl's book "Mastering Regular
52 Expressions", the standard algorithm is an "NFA algorithm". It conducts a
53 depth-first search of the pattern tree. That is, it proceeds along a single
54 path through the tree, checking that the subject matches what is required. When
55 there is a mismatch, the algorithm tries any alternatives at the current point,
56 and if they all fail, it backs up to the previous branch point in the tree, and
57 tries the next alternative branch at that level. This often involves backing up
58 (moving to the left) in the subject string as well. The order in which
59 repetition branches are tried is controlled by the greedy or ungreedy nature of
60 the quantifier.
61 .P
62 If a leaf node is reached, a matching string has been found, and at that point
63 the algorithm stops. Thus, if there is more than one possible match, this
64 algorithm returns the first one that it finds. Whether this is the shortest,
65 the longest, or some intermediate length depends on the way the greedy and
66 ungreedy repetition quantifiers are specified in the pattern.
67 .P
68 Because it ends up with a single path through the tree, it is relatively
69 straightforward for this algorithm to keep track of the substrings that are
70 matched by portions of the pattern in parentheses. This provides support for
71 capturing parentheses and back references.
72 .
73 .
74 .SH "THE ALTERNATIVE MATCHING ALGORITHM"
75 .rs
76 .sp
77 This algorithm conducts a breadth-first search of the tree. Starting from the
78 first matching point in the subject, it scans the subject string from left to
79 right, once, character by character, and as it does this, it remembers all the
80 paths through the tree that represent valid matches. In Friedl's terminology,
81 this is a kind of "DFA algorithm", though it is not implemented as a
82 traditional finite state machine (it keeps multiple states active
83 simultaneously).
84 .P
85 Although the general principle of this matching algorithm is that it scans the
86 subject string only once, without backtracking, there is one exception: when a
87 lookaround assertion is encountered, the characters following or preceding the
88 current point have to be independently inspected.
89 .P
90 The scan continues until either the end of the subject is reached, or there are
91 no more unterminated paths. At this point, terminated paths represent the
92 different matching possibilities (if there are none, the match has failed).
93 Thus, if there is more than one possible match, this algorithm finds all of
94 them, and in particular, it finds the longest. The matches are returned in
95 decreasing order of length. There is an option to stop the algorithm after the
96 first match (which is necessarily the shortest) is found.
97 .P
98 Note that all the matches that are found start at the same point in the
99 subject. If the pattern
100 .sp
101 cat(er(pillar)?)?
102 .sp
103 is matched against the string "the caterpillar catchment", the result will be
104 the three strings "caterpillar", "cater", and "cat" that start at the fifth
105 character of the subject. The algorithm does not automatically move on to find
106 matches that start at later positions.
107 .P
108 There are a number of features of PCRE regular expressions that are not
109 supported by the alternative matching algorithm. They are as follows:
110 .P
111 1. Because the algorithm finds all possible matches, the greedy or ungreedy
112 nature of repetition quantifiers is not relevant. Greedy and ungreedy
113 quantifiers are treated in exactly the same way. However, possessive
114 quantifiers can make a difference when what follows could also match what is
115 quantified, for example in a pattern like this:
116 .sp
117 ^a++\ew!
118 .sp
119 This pattern matches "aaab!" but not "aaa!", which would be matched by a
120 non-possessive quantifier. Similarly, if an atomic group is present, it is
121 matched as if it were a standalone pattern at the current point, and the
122 longest match is then "locked in" for the rest of the overall pattern.
123 .P
124 2. When dealing with multiple paths through the tree simultaneously, it is not
125 straightforward to keep track of captured substrings for the different matching
126 possibilities, and PCRE's implementation of this algorithm does not attempt to
127 do this. This means that no captured substrings are available.
128 .P
129 3. Because no substrings are captured, back references within the pattern are
130 not supported, and cause errors if encountered.
131 .P
132 4. For the same reason, conditional expressions that use a backreference as the
133 condition or test for a specific group recursion are not supported.
134 .P
135 5. Because many paths through the tree may be active, the \eK escape sequence,
136 which resets the start of the match when encountered (but may be on some paths
137 and not on others), is not supported. It causes an error if encountered.
138 .P
139 6. Callouts are supported, but the value of the \fIcapture_top\fP field is
140 always 1, and the value of the \fIcapture_last\fP field is always -1.
141 .P
142 7. The \eC escape sequence, which (in the standard algorithm) always matches a
143 single data unit, even in UTF-8 or UTF-16 modes, is not supported in these
144 modes, because the alternative algorithm moves through the subject string one
145 character (not data unit) at a time, for all active paths through the tree.
146 .P
147 8. Except for (*FAIL), the backtracking control verbs such as (*PRUNE) are not
148 supported. (*FAIL) is supported, and behaves like a failing negative assertion.
149 .
150 .
151 .SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"
152 .rs
153 .sp
154 Using the alternative matching algorithm provides the following advantages:
155 .P
156 1. All possible matches (at a single point in the subject) are automatically
157 found, and in particular, the longest match is found. To find more than one
158 match using the standard algorithm, you have to do kludgy things with
159 callouts.
160 .P
161 2. Because the alternative algorithm scans the subject string just once, and
162 never needs to backtrack (except for lookbehinds), it is possible to pass very
163 long subject strings to the matching function in several pieces, checking for
164 partial matching each time. Although it is possible to do multi-segment
165 matching using the standard algorithm by retaining partially matched
166 substrings, it is more complicated. The
167 .\" HREF
168 \fBpcrepartial\fP
169 .\"
170 documentation gives details of partial matching and discusses multi-segment
171 matching.
172 .
173 .
174 .SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"
175 .rs
176 .sp
177 The alternative algorithm suffers from a number of disadvantages:
178 .P
179 1. It is substantially slower than the standard algorithm. This is partly
180 because it has to search for all possible matches, but is also because it is
181 less susceptible to optimization.
182 .P
183 2. Capturing parentheses and back references are not supported.
184 .P
185 3. Although atomic groups are supported, their use does not provide the
186 performance advantage that it does for the standard algorithm.
187 .
188 .
189 .SH AUTHOR
190 .rs
191 .sp
192 .nf
193 Philip Hazel
194 University Computing Service
195 Cambridge CB2 3QH, England.
196 .fi
197 .
198 .
199 .SH REVISION
200 .rs
201 .sp
202 .nf
203 Last updated: 08 January 2012
204 Copyright (c) 1997-2012 University of Cambridge.
205 .fi

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