1 
.TH PCREMATCHING 3

2 
.SH NAME

3 
PCRE  Perlcompatible 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 
Perlcompatible 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 Perlcompatible. 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: depthfirst and breadthfirst, 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 
depthfirst 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 breadthfirst 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 
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 
supported by the alternative matching algorithm. They are as follows:

97 
.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 
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 
nonpossessive 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 
.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 
condition or test for a specific group recursion are not supported.

121 
.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 
byte, even in UTF8 mode, is not supported because the alternative algorithm

128 
moves through the subject string one character at a time, for all active paths

129 
through the tree.

130 
.

131 
.SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"

132 
.rs

133 
.sp

134 
Using the alternative matching algorithm provides the following advantages:

135 
.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 
matching do not apply to the alternative algorithm. For nonanchored patterns,

144 
the starting position of a partial match is available.

145 
.P

146 
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 
.

151 
.SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"

152 
.rs

153 
.sp

154 
The alternative algorithm suffers from a number of disadvantages:

155 
.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 
3. Although atomic groups are supported, their use does not provide the

163 
performance advantage that it does for the standard algorithm.

164 
.

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) 19972007 University of Cambridge.

182 
.fi
