pcrematching


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-
       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).

       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.

       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.  The  matches are returned in decreasing order of length. There is
       an option to stop the algorithm after the first match (which is  neces-
       sarily the shortest) is 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 "caterpillar", "cater", and "cat" that start
       at the fifth character of the subject. The algorithm does not automati-
       cally 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-
       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.

       8. Except for (*FAIL), the backtracking control verbs such as  (*PRUNE)
       are  not  supported.  (*FAIL)  is supported, and behaves like a failing
       negative assertion.

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. 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 (pcre_exec()), by retain-
       ing  partially matched substrings, it is more complicated. The pcrepar-
       tial documentation gives details  of  partial  matching  and  discusses
       multi-segment matching.

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
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