pcre2matching

PCRE2MATCHING(3)           Library Functions Manual           PCRE2MATCHING(3)

NAME
       PCRE2 - Perl-compatible regular expressions (revised API)

PCRE2 MATCHING ALGORITHMS

       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
       pcre2_match() 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 pcre2jit documenta-
       tion is compatible with this function.

       An alternative algorithm is provided by the pcre2_dfa_match() function;
       it operates in a different way, and is not Perl-compatible. This alter-
       native  has advantages and disadvantages compared with the standard al-
       gorithm, 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 PCRE2.

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 alternations and the greedy or ungreedy repetition quan-
       tifiers 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 backreferences.

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 in-
       spected.

       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 the output vector 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 the size of vector needed to contain all the results depends
       on the number of simultaneous matches, not on the number of parentheses
       in  the pattern. Using pcre2_match_data_create_from_pattern() to create
       the match data block is therefore not advisable when doing  DFA  match-
       ing.

       Note  also  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
       is  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.

       PCRE2's "auto-possessification" optimization usually applies to charac-
       ter repeats at the end of a pattern (as well as internally). For  exam-
       ple, 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 PCRE2_NO_AUTO_POS-
       SESS option when compiling.

       There are a number of features of PCRE2 regular  expressions  that  are
       not  supported  or behave differently in the alternative matching func-
       tion. Those that are not supported cause an error if encountered.

       1. Because the algorithm finds all possible matches, the greedy or  un-
       greedy  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:

         ^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 PCRE2'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, backreferences within  the  pat-
       tern are not supported.

       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. Again for the same reason, script runs are not supported.

       6. Because many paths through the tree may be active, the \K escape se-
       quence, which resets the start of the match when encountered  (but  may
       be on some paths and not on others), is not supported.

       7.  Callouts  are  supported, but the value of the capture_top field is
       always 1, and the value of the capture_last field is always 0.

       8. The \C 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  sub-
       ject  string  one  character  (not code unit) at a time, for all active
       paths through the tree.

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

       10. The PCRE2_MATCH_INVALID_UTF option for pcre2_compile() is not  sup-
       ported by pcre2_dfa_match().

ADVANTAGES OF THE ALTERNATIVE ALGORITHM

       The  main  advantage  of the alternative algorithm is that 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
       at the same point using the standard algorithm, you have to  do  kludgy
       things with callouts.

       Partial  matching  is  possible with this algorithm, though it has some
       limitations. The pcre2partial 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,  backreferences,  script runs, and matching
       within invalid UTF string are not supported.

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

       4. JIT optimization is not supported.

AUTHOR

       Philip Hazel
       Retired from University Computing Service
       Cambridge, England.

REVISION

       Last updated: 28 August 2021
       Copyright (c) 1997-2021 University of Cambridge.

PCRE2 10.38                     28 August 2021                PCRE2MATCHING(3)