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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 ph10 461 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 ph10 456 current point have to be independently inspected.
81     .P
82 nigel 77 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 ph10 572 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 nigel 77 .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 ph10 572 cat(er(pillar)?)?
94 nigel 77 .sp
95     is matched against the string "the caterpillar catchment", the result will be
96 ph10 572 the three strings "caterpillar", "cater", and "cat" that start at the fifth
97 nigel 77 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 nigel 93 supported by the alternative matching algorithm. They are as follows:
102 nigel 77 .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 nigel 93 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 nigel 77 .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 nigel 93 condition or test for a specific group recursion are not supported.
126 nigel 77 .P
127 ph10 168 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 nigel 77 always 1, and the value of the \fIcapture_last\fP field is always -1.
133     .P
134 ph10 210 7. The \eC escape sequence, which (in the standard algorithm) matches a single
135 nigel 93 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 nigel 77 through the tree.
138 ph10 210 .P
139 ph10 341 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 nigel 77 .
142 nigel 93 .SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"
143 nigel 77 .rs
144     .sp
145 nigel 93 Using the alternative matching algorithm provides the following advantages:
146 nigel 77 .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 ph10 426 2. Because the alternative algorithm scans the subject string just once, and
153 nigel 93 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 ph10 572 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 ph10 461 .\" HREF
159 ph10 456 \fBpcrepartial\fP
160 ph10 461 .\"
161 ph10 553 documentation gives details of partial matching and discusses multi-segment
162     matching.
163 nigel 77 .
164 ph10 456 .
165 nigel 93 .SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"
166 nigel 77 .rs
167     .sp
168 nigel 93 The alternative algorithm suffers from a number of disadvantages:
169 nigel 77 .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 nigel 93 3. Although atomic groups are supported, their use does not provide the
177     performance advantage that it does for the standard algorithm.
178 ph10 99 .
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 ph10 572 Last updated: 17 November 2010
195 ph10 553 Copyright (c) 1997-2010 University of Cambridge.
196 ph10 99 .fi

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