trunk/doc/pcrematching.3

.TH PCREMATCHING 3
.SH NAME
PCRE - Perl-compatible regular expressions
.SH "PCRE MATCHING ALGORITHMS"
.rs
.sp
This document describes the two different algorithms that are available in PCRE
for matching a compiled regular expression against a given subject string. The
"standard" algorithm is the one provided by the \fBpcre_exec()\fP function.
This works in the same was as Perl's matching function, and provides a
Perl-compatible matching operation.
.P
An alternative algorithm is provided by the \fBpcre_dfa_exec()\fP function;
this operates in a different way, and is not Perl-compatible. It has advantages
and disadvantages compared with the standard algorithm, and these are described
below.
.P
When there is only one possible way in which a given subject string can match a
pattern, the two algorithms give the same answer. A difference arises, however,
when there are multiple possibilities. For example, if the pattern
.sp
  ^<.*>
.sp
is matched against the string
.sp
  <something> <something else> <something further>
.sp
there are three possible answers. The standard algorithm finds only one of
them, whereas the alternative algorithm finds all three.
.
.SH "REGULAR EXPRESSIONS AS TREES"
.rs
.sp
The set of strings that are matched by a regular expression can be represented
as a tree structure. An unlimited repetition in the pattern makes the tree of
infinite size, but it is still a tree. Matching the pattern to a given subject
string (from a given starting point) can be thought of as a search of the tree.
There are two ways to search a tree: depth-first and breadth-first, and these
correspond to the two matching algorithms provided by PCRE.
.
.SH "THE STANDARD MATCHING ALGORITHM"
.rs
.sp
In the terminology of Jeffrey Friedl's book "Mastering Regular
Expressions", the standard algorithm is an "NFA algorithm". It conducts a
depth-first search of the pattern tree. That is, it proceeds along a single
path through the tree, checking that the subject matches what is required. When
there is a mismatch, the algorithm tries any alternatives at the current point,
and if they all fail, it backs up to the previous branch point in the tree, and
tries the next alternative branch at that level. This often involves backing up
(moving to the left) in the subject string as well. The order in which
repetition branches are tried is controlled by the greedy or ungreedy nature of
the quantifier.
.P
If a leaf node is reached, a matching string has been found, and at that point
the algorithm stops. Thus, if there is more than one possible match, this
algorithm returns the first one that it finds. Whether this is the shortest,
the longest, or some intermediate length depends on the way the greedy and
ungreedy repetition quantifiers are specified in the pattern.
.P
Because it ends up with a single path through the tree, it is relatively
straightforward for this algorithm to keep track of the substrings that are
matched by portions of the pattern in parentheses. This provides support for
capturing parentheses and back references.
.
.SH "THE ALTERNATIVE MATCHING ALGORITHM"
.rs
.sp
This algorithm conducts a breadth-first search of the tree. Starting from the
first matching point in the subject, it scans the subject string from left to
right, once, character by character, and as it does this, it remembers all the
paths through the tree that represent valid matches. In Friedl's terminology,
this is a kind of "DFA algorithm", though it is not implemented as a
traditional finite state machine (it keeps multiple states active
simultaneously).
.P
Although the general principle of this matching algorithm is that it scans the 
subject string only once, without backtracking, there is one exception: when a 
lookaround assertion is encountered, the characters following or preceding the 
current point have to be independently inspected.
.P
The scan continues until either the end of the subject is reached, or there are
no more unterminated paths. At this point, terminated paths represent the
different matching possibilities (if there are none, the match has failed).
Thus, if there is more than one possible match, this algorithm finds all of
them, and in particular, it finds the longest. There is an option to stop the
algorithm after the first match (which is necessarily the shortest) is found.
.P
Note that all the matches that are found start at the same point in the
subject. If the pattern
.sp
  cat(er(pillar)?)
.sp
is matched against the string "the caterpillar catchment", the result will be
the three strings "cat", "cater", and "caterpillar" that start at the fourth
character of the subject. The algorithm does not automatically move on to find
matches that start at later positions.
.P
There are a number of features of PCRE regular expressions that are not
supported by the alternative matching algorithm. They are as follows:
.P
1. Because the algorithm finds all possible matches, the greedy or ungreedy
nature of repetition quantifiers is not relevant. Greedy and ungreedy
quantifiers are treated in exactly the same way. However, possessive
quantifiers can make a difference when what follows could also match what is
quantified, for example in a pattern like this:
.sp
  ^a++\ew!
.sp
This pattern matches "aaab!" but not "aaa!", which would be matched by a
non-possessive quantifier. Similarly, if an atomic group is present, it is
matched as if it were a standalone pattern at the current point, and the
longest match is then "locked in" for the rest of the overall pattern.
.P
2. When dealing with multiple paths through the tree simultaneously, it is not
straightforward to keep track of captured substrings for the different matching
possibilities, and PCRE's implementation of this algorithm does not attempt to
do this. This means that no captured substrings are available.
.P
3. Because no substrings are captured, back references within the pattern are
not supported, and cause errors if encountered.
.P
4. For the same reason, conditional expressions that use a backreference as the
condition or test for a specific group recursion are not supported.
.P
5. Because many paths through the tree may be active, the \eK escape sequence,
which resets the start of the match when encountered (but may be on some paths
and not on others), is not supported. It causes an error if encountered.
.P
6. Callouts are supported, but the value of the \fIcapture_top\fP field is
always 1, and the value of the \fIcapture_last\fP field is always -1.
.P
7. The \eC escape sequence, which (in the standard algorithm) matches a single
byte, even in UTF-8 mode, is not supported because the alternative algorithm
moves through the subject string one character at a time, for all active paths
through the tree.
.P
8. Except for (*FAIL), the backtracking control verbs such as (*PRUNE) are not
supported. (*FAIL) is supported, and behaves like a failing negative assertion.
.
.SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"
.rs
.sp
Using the alternative matching algorithm provides the following advantages:
.P
1. All possible matches (at a single point in the subject) are automatically
found, and in particular, the longest match is found. To find more than one
match using the standard algorithm, you have to do kludgy things with
callouts.
.P
2. Because the alternative algorithm scans the subject string just once, and
never needs to backtrack, it is possible to pass very long subject strings to
the matching function in several pieces, checking for partial matching each
time. The
.\" HREF                                                                
\fBpcrepartial\fP
.\"                                                           
documentation gives details of partial matching.
.
.
.SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"
.rs
.sp
The alternative algorithm suffers from a number of disadvantages:
.P
1. It is substantially slower than the standard algorithm. This is partly
because it has to search for all possible matches, but is also because it is
less susceptible to optimization.
.P
2. Capturing parentheses and back references are not supported.
.P
3. Although atomic groups are supported, their use does not provide the
performance advantage that it does for the standard algorithm.
.
.
.SH AUTHOR
.rs
.sp
.nf
Philip Hazel
University Computing Service
Cambridge CB2 3QH, England.
.fi
.
.
.SH REVISION
.rs
.sp
.nf
Last updated: 29 September 2009
Copyright (c) 1997-2009 University of Cambridge.
.fi
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	456	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	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	456	them, and in particular, it finds the longest. There is an option to stop the
87			algorithm after the first match (which is necessarily the shortest) is found.
88	nigel	77	.P
89			Note that all the matches that are found start at the same point in the
90			subject. If the pattern
91			.sp
92			cat(er(pillar)?)
93			.sp
94			is matched against the string "the caterpillar catchment", the result will be
95			the three strings "cat", "cater", and "caterpillar" that start at the fourth
96			character of the subject. The algorithm does not automatically move on to find
97			matches that start at later positions.
98			.P
99			There are a number of features of PCRE regular expressions that are not
100	nigel	93	supported by the alternative matching algorithm. They are as follows:
101	nigel	77	.P
102			1. Because the algorithm finds all possible matches, the greedy or ungreedy
103			nature of repetition quantifiers is not relevant. Greedy and ungreedy
104	nigel	93	quantifiers are treated in exactly the same way. However, possessive
105			quantifiers can make a difference when what follows could also match what is
106			quantified, for example in a pattern like this:
107			.sp
108			^a++\ew!
109			.sp
110			This pattern matches "aaab!" but not "aaa!", which would be matched by a
111			non-possessive quantifier. Similarly, if an atomic group is present, it is
112			matched as if it were a standalone pattern at the current point, and the
113			longest match is then "locked in" for the rest of the overall pattern.
114	nigel	77	.P
115			2. When dealing with multiple paths through the tree simultaneously, it is not
116			straightforward to keep track of captured substrings for the different matching
117			possibilities, and PCRE's implementation of this algorithm does not attempt to
118			do this. This means that no captured substrings are available.
119			.P
120			3. Because no substrings are captured, back references within the pattern are
121			not supported, and cause errors if encountered.
122			.P
123			4. For the same reason, conditional expressions that use a backreference as the
124	nigel	93	condition or test for a specific group recursion are not supported.
125	nigel	77	.P
126	ph10	168	5. Because many paths through the tree may be active, the \eK escape sequence,
127			which resets the start of the match when encountered (but may be on some paths
128			and not on others), is not supported. It causes an error if encountered.
129			.P
130			6. Callouts are supported, but the value of the \fIcapture_top\fP field is
131	nigel	77	always 1, and the value of the \fIcapture_last\fP field is always -1.
132			.P
133	ph10	210	7. The \eC escape sequence, which (in the standard algorithm) matches a single
134	nigel	93	byte, even in UTF-8 mode, is not supported because the alternative algorithm
135			moves through the subject string one character at a time, for all active paths
136	nigel	77	through the tree.
137	ph10	210	.P
138	ph10	341	8. Except for (FAIL), the backtracking control verbs such as (PRUNE) are not
139			supported. (*FAIL) is supported, and behaves like a failing negative assertion.
140	nigel	77	.
141	nigel	93	.SH "ADVANTAGES OF THE ALTERNATIVE ALGORITHM"
142	nigel	77	.rs
143			.sp
144	nigel	93	Using the alternative matching algorithm provides the following advantages:
145	nigel	77	.P
146			1. All possible matches (at a single point in the subject) are automatically
147			found, and in particular, the longest match is found. To find more than one
148			match using the standard algorithm, you have to do kludgy things with
149			callouts.
150			.P
151	ph10	426	2. Because the alternative algorithm scans the subject string just once, and
152	nigel	93	never needs to backtrack, it is possible to pass very long subject strings to
153			the matching function in several pieces, checking for partial matching each
154	ph10	456	time. The
155			.\" HREF
156			\fBpcrepartial\fP
157			.\"
158			documentation gives details of partial matching.
159	nigel	77	.
160	ph10	456	.
161	nigel	93	.SH "DISADVANTAGES OF THE ALTERNATIVE ALGORITHM"
162	nigel	77	.rs
163			.sp
164	nigel	93	The alternative algorithm suffers from a number of disadvantages:
165	nigel	77	.P
166			1. It is substantially slower than the standard algorithm. This is partly
167			because it has to search for all possible matches, but is also because it is
168			less susceptible to optimization.
169			.P
170			2. Capturing parentheses and back references are not supported.
171			.P
172	nigel	93	3. Although atomic groups are supported, their use does not provide the
173			performance advantage that it does for the standard algorithm.
174	ph10	99	.
175			.
176			.SH AUTHOR
177			.rs
178			.sp
179			.nf
180			Philip Hazel
181			University Computing Service
182			Cambridge CB2 3QH, England.
183			.fi
184			.
185			.
186			.SH REVISION
187			.rs
188			.sp
189			.nf
190	ph10	456	Last updated: 29 September 2009
191	ph10	426	Copyright (c) 1997-2009 University of Cambridge.
192	ph10	99	.fi
Name	Value
svn:eol-style	native
svn:keywords	"Author Date Id Revision Url"