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NAME

       PCRE - Perl-compatible regular expressions


PCRE MATCHING ALGORITHMS


       This document describes the two different algorithms that are available
       in PCRE for matching a compiled regular expression against a given sub-
       ject  string.  The  "standard"  algorithm  is  the  one provided by the
       pcre_exec() function.  This works in the same was  as  Perl's  matching
       function, and provides a Perl-compatible matching operation.

       An  alternative  algorithm is provided by the pcre_dfa_exec() 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.

       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

         ^<.*>

       is matched against the string

         <something> <something else> <something further>

       there are three possible answers. The standard algorithm finds only one
       of them, whereas the alternative algorithm finds all three.


REGULAR EXPRESSIONS AS TREES


       The set of strings that are matched by a regular expression can be rep-
       resented  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.


THE STANDARD MATCHING ALGORITHM


       In the terminology of Jeffrey Friedl's book "Mastering Regular  Expres-
       sions",  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  alterna-
       tives  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.

       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 possi-
       ble 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.

       Because  it  ends  up  with a single path through the tree, it is rela-
       tively straightforward for this algorithm to keep  track  of  the  sub-
       strings  that  are  matched  by portions of the pattern in parentheses.
       This provides support for capturing parentheses and back references.


THE ALTERNATIVE MATCHING ALGORITHM


       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).

       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 long-
       est.  In PCRE, there is an option to stop the algorithm after the first
       match (which is necessarily the shortest) has been found.

       Note that all the matches that are found start at the same point in the
       subject. If the pattern

         cat(er(pillar)?)

       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 automat-
       ically move on to find matches that start at later positions.

       There are a number of features of PCRE regular expressions that are not
       supported by the alternative matching algorithm. They are as follows:

       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, pos-
       sessive quantifiers can make a difference when what follows could  also
       match what is quantified, for example in a pattern like this:

         ^a++\w!

       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.

       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 sub-
       strings are available.

       3.  Because no substrings are captured, back references within the pat-
       tern are not supported, and cause errors if encountered.

       4. For the same reason, conditional expressions that use  a  backrefer-
       ence  as  the  condition or test for a specific group recursion are not
       supported.

       5. Because many paths through the tree may be  active,  the  \K  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.

       6.  Callouts  are  supported, but the value of the capture_top field is
       always 1, and the value of the capture_last field is always -1.

       7.  The \C escape sequence, which (in the standard algorithm) matches a
       single  byte, even in UTF-8 mode, is not supported because the alterna-
       tive algorithm moves through the subject  string  one  character  at  a
       time, for all active paths through the tree.


ADVANTAGES OF THE ALTERNATIVE ALGORITHM


       Using  the alternative matching algorithm provides the following advan-
       tages:

       1. All possible matches (at a single point in the subject) are automat-
       ically  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.

       2.  There is much better support for partial matching. The restrictions
       on the content of the pattern that apply when using the standard  algo-
       rithm  for  partial matching do not apply to the alternative algorithm.
       For non-anchored patterns, the starting position of a partial match  is
       available.

       3.  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.


DISADVANTAGES OF THE ALTERNATIVE ALGORITHM


       The alternative algorithm suffers from a number of disadvantages:

       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.

       2. Capturing parentheses and back references are not supported.

       3. Although atomic groups are supported, their use does not provide the
       performance advantage that it does for the standard algorithm.


AUTHOR


       Philip Hazel
       University Computing Service
       Cambridge CB2 3QH, England.


REVISION


       Last updated: 29 May 2007
       Copyright (c) 1997-2007 University of Cambridge.

                                                               PCREMATCHING(3)

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