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           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.


           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.


           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
           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
           longest.  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
           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:
           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
           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-
           time, for all active paths through the tree.
           8.  Except for (*FAIL), the backtracking control verbs such as (*PRUNE)
           are not supported. (*FAIL) is supported, and  behaves  like  a  failing
           negative assertion.


           Using  the alternative matching algorithm provides the following advan-
           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
           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.


           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.


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


           Last updated: 19 April 2008
           Copyright (c) 1997-2008 University of Cambridge.

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