| .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. The matches are returned in |
| decreasing order of length. 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 "caterpillar", "cater", and "cat" that start at the fifth |
| 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 in UTF-8 mode, 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. Although it is possible to do multi-segment matching using the standard |
| algorithm (\fBpcre_exec()\fP), by retaining partially matched substrings, it is |
| more complicated. The |
| .\" HREF |
| \fBpcrepartial\fP |
| .\" |
| documentation gives details of partial matching and discusses multi-segment |
| 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: 19 November 2011 |
| Copyright (c) 1997-2010 University of Cambridge. |
| .fi |