# pcre2matching

## 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
           way as Perl's matching function, and provides a Perl-compatible
           matching operation. The just-in-time (JIT) optimization that is
           described in the **pcre2jit** documentation 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 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 anchored 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 PCRE2.
    


## 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 alternations and the
           greedy or 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
           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 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 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 capturing parentheses in the pattern. Using
           **pcre2_match_data_create_from_pattern()** to create the match data
           block is therefore not advisable when doing DFA matching.
    
           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 automatically move on to find matches that start at later
           positions.
    
           PCRE2'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 PCRE2_NO_AUTO_POSSESS option when compiling.
    
           There are a number of features of PCRE2 regular expressions that
           are not supported or behave differently in the alternative
           matching function. Those that are not supported cause an error if
           encountered.
    
           1. Because the algorithm finds all possible matches, the greedy or
           ungreedy 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 substrings are available.
    
           3. Because no substrings are captured, a number of related
           features are not available:
    
           (a) Backreferences;
    
           (b) Conditional expressions that use a backreference as the
           condition or test for a specific group recursion;
    
           (c) Script runs;
    
           (d) Scan substring assertions.
    
           4. 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.
    
           5. 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.
    
           6. The \C escape sequence, which (in the standard algorithm)
           always matches a single code unit, even in a UTF mode, is not
           supported in UTF modes because the alternative algorithm moves
           through the subject string one character (not code unit) at a
           time, for all active paths through the tree.
    
           7. Except for (*FAIL), the backtracking control verbs such as
           (*PRUNE) are not supported. (*FAIL) is supported, and behaves like
           a failing negative assertion.
    
           8. The PCRE2_MATCH_INVALID_UTF option for **pcre2_compile()** is not
           supported 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 and other features such as backreferences
           that rely on them are not supported.
    
           3. Matching within invalid UTF strings is not supported.
    
           4. Although atomic groups are supported, their use does not
           provide the performance advantage that it does for the standard
           algorithm.
    
           5. JIT optimization is not supported.
    


## REVISION



    
           Last updated: 30 August 2024
           Copyright (c) 1997-2024 University of Cambridge.
    


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