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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  subject  string.  The  "standard"
       algorithm  is  the  one  provided  by  the  pcre_exec(),  pcre16_exec()  and pcre32_exec()
       functions. These work 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 pcrejit documentation is compatible with these functions.

       An alternative  algorithm  is  provided  by  the  pcre_dfa_exec(),  pcre16_dfa_exec()  and
       pcre32_dfa_exec() functions; they operate in a different way, and are not Perl-compatible.
       This alternative 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 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.

THE STANDARD MATCHING ALGORITHM


       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.

       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.

       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.

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).

       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 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.

       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 automatically move on to find matches that start at later
       positions.

       PCRE's "auto-possessification" optimization usually applies to character  repeats  at  the
       end  of  a pattern (as well as internally). For example, the pattern "a\d+" is compiled as
       if it were "a\d++"  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\d+?") or set the PCRE_NO_AUTO_POSSESS option when compiling.

       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, possessive 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 substrings are available.

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

       4. For the same reason, conditional expressions that use a backreference 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) always matches a single  data
       unit,  even in UTF-8, UTF-16 or UTF-32 modes, is not supported in these modes, because the
       alternative algorithm moves through the subject string one character (not data unit) 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 advantages:

       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.

       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  possible  to  do  multi-segment matching using the standard algorithm by retaining
       partially matched substrings, it is more complicated. The pcrepartial 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


       Last updated: 12 November 2013
       Copyright (c) 1997-2012 University of Cambridge.