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 DFA 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 \fIMastering Regular
Expressions\fP, 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 DFA MATCHING ALGORITHM"
.rs
.sp
DFA stands for "deterministic finite automaton", but you do not need to
understand the origins of that name. 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.
.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. In PCRE, there is an option to
stop the algorithm after the first match (which is necessarily the shortest)
has been 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 DFA 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.
.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 are not supported.
.P
5. 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
6.
The \eC escape sequence, which (in the standard algorithm) matches a single
byte, even in UTF-8 mode, is not supported because the DFA algorithm moves
through the subject string one character at a time, for all active paths
through the tree.
.
.SH "ADVANTAGES OF THE DFA ALGORITHM"
.rs
.sp
Using the DFA 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. There is much better support for partial matching. The restrictions on the
content of the pattern that apply when using the standard algorithm for partial
matching do not apply to the DFA algorithm. For non-anchored patterns, the
starting position of a partial match is available.
.P
3. Because the DFA 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.
.
.SH "DISADVANTAGES OF THE DFA ALGORITHM"
.rs
.sp
The DFA 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. The "atomic group" feature of PCRE regular expressions is supported, but
does not provide the advantage that it does for the standard algorithm.
.P
.in 0
Last updated: 06 June 2006
.br
Copyright (c) 1997-2006 University of Cambridge.
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 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	them, whereas the DFA 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: depth-first and breadth-first, 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 \fIMastering Regular
45	Expressions\fP, the standard algorithm is an "NFA algorithm". It conducts a
46	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	.SH "THE DFA MATCHING ALGORITHM"
67	.rs
68	.sp
69	DFA stands for "deterministic finite automaton", but you do not need to
70	understand the origins of that name. This algorithm conducts a breadth-first
71	search of the tree. Starting from the first matching point in the subject, it
72	scans the subject string from left to right, once, character by character, and
73	as it does this, it remembers all the paths through the tree that represent
74	valid matches.
75	.P
76	The scan continues until either the end of the subject is reached, or there are
77	no more unterminated paths. At this point, terminated paths represent the
78	different matching possibilities (if there are none, the match has failed).
79	Thus, if there is more than one possible match, this algorithm finds all of
80	them, and in particular, it finds the longest. In PCRE, there is an option to
81	stop the algorithm after the first match (which is necessarily the shortest)
82	has been found.
83	.P
84	Note that all the matches that are found start at the same point in the
85	subject. If the pattern
86	.sp
87	cat(er(pillar)?)
88	.sp
89	is matched against the string "the caterpillar catchment", the result will be
90	the three strings "cat", "cater", and "caterpillar" that start at the fourth
91	character of the subject. The algorithm does not automatically move on to find
92	matches that start at later positions.
93	.P
94	There are a number of features of PCRE regular expressions that are not
95	supported by the DFA matching algorithm. They are as follows:
96	.P
97	1. Because the algorithm finds all possible matches, the greedy or ungreedy
98	nature of repetition quantifiers is not relevant. Greedy and ungreedy
99	quantifiers are treated in exactly the same way.
100	.P
101	2. When dealing with multiple paths through the tree simultaneously, it is not
102	straightforward to keep track of captured substrings for the different matching
103	possibilities, and PCRE's implementation of this algorithm does not attempt to
104	do this. This means that no captured substrings are available.
105	.P
106	3. Because no substrings are captured, back references within the pattern are
107	not supported, and cause errors if encountered.
108	.P
109	4. For the same reason, conditional expressions that use a backreference as the
110	condition are not supported.
111	.P
112	5. Callouts are supported, but the value of the \fIcapture_top\fP field is
113	always 1, and the value of the \fIcapture_last\fP field is always -1.
114	.P
115	6.
116	The \eC escape sequence, which (in the standard algorithm) matches a single
117	byte, even in UTF-8 mode, is not supported because the DFA algorithm moves
118	through the subject string one character at a time, for all active paths
119	through the tree.
120	.
121	.SH "ADVANTAGES OF THE DFA ALGORITHM"
122	.rs
123	.sp
124	Using the DFA matching algorithm provides the following advantages:
125	.P
126	1. All possible matches (at a single point in the subject) are automatically
127	found, and in particular, the longest match is found. To find more than one
128	match using the standard algorithm, you have to do kludgy things with
129	callouts.
130	.P
131	2. There is much better support for partial matching. The restrictions on the
132	content of the pattern that apply when using the standard algorithm for partial
133	matching do not apply to the DFA algorithm. For non-anchored patterns, the
134	starting position of a partial match is available.
135	.P
136	3. Because the DFA algorithm scans the subject string just once, and never
137	needs to backtrack, it is possible to pass very long subject strings to the
138	matching function in several pieces, checking for partial matching each time.
139	.
140	.SH "DISADVANTAGES OF THE DFA ALGORITHM"
141	.rs
142	.sp
143	The DFA algorithm suffers from a number of disadvantages:
144	.P
145	1. It is substantially slower than the standard algorithm. This is partly
146	because it has to search for all possible matches, but is also because it is
147	less susceptible to optimization.
148	.P
149	2. Capturing parentheses and back references are not supported.
150	.P
151	3. The "atomic group" feature of PCRE regular expressions is supported, but
152	does not provide the advantage that it does for the standard algorithm.
153	.P
154	.in 0
155	Last updated: 06 June 2006
156	.br
157	Copyright (c) 1997-2006 University of Cambridge.