| .TH PCRE2MATCHING 3 "29 September 2014" "PCRE2 10.00" |
| .SH NAME |
| PCRE2 - Perl-compatible regular expressions (revised API) |
| .SH "PCRE2 MATCHING ALGORITHMS" |
| .rs |
| .sp |
| This document describes the two different algorithms that are available in |
| PCRE2 for matching a compiled regular expression against a given subject |
| string. The "standard" algorithm is the one provided by the \fBpcre2_match()\fP |
| function. This works in the same as as Perl's matching function, and provide a |
| Perl-compatible matching operation. The just-in-time (JIT) optimization that is |
| described in the |
| .\" HREF |
| \fBpcre2jit\fP |
| .\" |
| documentation is compatible with this function. |
| .P |
| An alternative algorithm is provided by the \fBpcre2_dfa_match()\fP function; |
| it operates in a different way, and is not Perl-compatible. This alternative |
| 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 PCRE2. |
| . |
| . |
| .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 is 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 |
| PCRE2's "auto-possessification" optimization usually applies to character |
| repeats at the end of a pattern (as well as internally). For example, the |
| pattern "a\ed+" is compiled as if it were "a\ed++" because there is no point |
| even considering the possibility of backtracking into the repeated digits. For |
| DFA matching, this means that only one possible match is found. If you really |
| do want multiple matches in such cases, either use an ungreedy repeat |
| ("a\ed+?") or set the PCRE2_NO_AUTO_POSSESS option when compiling. |
| .P |
| There are a number of features of PCRE2 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 (though it may affect |
| auto-possessification, as just described). During matching, 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 PCRE2'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 0. |
| .P |
| 7. The \eC escape sequence, which (in the standard algorithm) always matches a |
| single code unit, even in a UTF mode, is not supported in these modes, because |
| the alternative algorithm moves through the subject string one character (not |
| code unit) 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 (except for lookbehinds), 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 also possible to do multi-segment |
| matching using the standard algorithm, by retaining partially matched |
| substrings, it is more complicated. The |
| .\" HREF |
| \fBpcre2partial\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, England. |
| .fi |
| . |
| . |
| .SH REVISION |
| .rs |
| .sp |
| .nf |
| Last updated: 29 September 2014 |
| Copyright (c) 1997-2014 University of Cambridge. |
| .fi |