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*Sat Apr 19 16:41:04 2008 UTC*
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Fix DFA (?!) bug; add support for JavaScript empty classes.

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 | 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 | nigel | 93 | supported by the alternative matching algorithm. They are as follows: |

97 | nigel | 77 | .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 | nigel | 93 | 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 | non-possessive 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 | nigel | 77 | .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 | nigel | 93 | condition or test for a specific group recursion are not supported. |

121 | nigel | 77 | .P |

122 | ph10 | 168 | 5. Because many paths through the tree may be active, the \eK escape sequence, |

123 | which resets the start of the match when encountered (but may be on some paths | ||

124 | and not on others), is not supported. It causes an error if encountered. | ||

125 | .P | ||

126 | 6. Callouts are supported, but the value of the \fIcapture_top\fP field is | ||

127 | nigel | 77 | always 1, and the value of the \fIcapture_last\fP field is always -1. |

128 | .P | ||

129 | ph10 | 210 | 7. The \eC escape sequence, which (in the standard algorithm) matches a single |

130 | nigel | 93 | byte, even in UTF-8 mode, is not supported because the alternative algorithm |

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

132 | nigel | 77 | through the tree. |

133 | ph10 | 210 | .P |

134 | ph10 | 341 | 8. Except for (*FAIL), the backtracking control verbs such as (*PRUNE) are not |

135 | supported. (*FAIL) is supported, and behaves like a failing negative assertion. | ||

136 | nigel | 77 | . |

137 | nigel | 93 | .SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM" |

138 | nigel | 77 | .rs |

139 | .sp | ||

140 | nigel | 93 | Using the alternative matching algorithm provides the following advantages: |

141 | nigel | 77 | .P |

142 | 1. All possible matches (at a single point in the subject) are automatically | ||

143 | found, and in particular, the longest match is found. To find more than one | ||

144 | match using the standard algorithm, you have to do kludgy things with | ||

145 | callouts. | ||

146 | .P | ||

147 | 2. There is much better support for partial matching. The restrictions on the | ||

148 | content of the pattern that apply when using the standard algorithm for partial | ||

149 | nigel | 93 | matching do not apply to the alternative algorithm. For non-anchored patterns, |

150 | the starting position of a partial match is available. | ||

151 | nigel | 77 | .P |

152 | nigel | 93 | 3. 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. | ||

156 | nigel | 77 | . |

157 | nigel | 93 | .SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM" |

158 | nigel | 77 | .rs |

159 | .sp | ||

160 | nigel | 93 | The alternative algorithm suffers from a number of disadvantages: |

161 | nigel | 77 | .P |

162 | 1. It is substantially slower than the standard algorithm. This is partly | ||

163 | because it has to search for all possible matches, but is also because it is | ||

164 | less susceptible to optimization. | ||

165 | .P | ||

166 | 2. Capturing parentheses and back references are not supported. | ||

167 | .P | ||

168 | nigel | 93 | 3. Although atomic groups are supported, their use does not provide the |

169 | performance advantage that it does for the standard algorithm. | ||

170 | ph10 | 99 | . |

171 | . | ||

172 | .SH AUTHOR | ||

173 | .rs | ||

174 | .sp | ||

175 | .nf | ||

176 | Philip Hazel | ||

177 | University Computing Service | ||

178 | Cambridge CB2 3QH, England. | ||

179 | .fi | ||

180 | . | ||

181 | . | ||

182 | .SH REVISION | ||

183 | .rs | ||

184 | .sp | ||

185 | .nf | ||

186 | ph10 | 341 | Last updated: 19 April 2008 |

187 | Copyright (c) 1997-2008 University of Cambridge. | ||

188 | ph10 | 99 | .fi |

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