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 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 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- 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 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 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: 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 sequence, 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. 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 (except for lookbehinds), it is pos- sible to pass very long subject strings to the matching function in several pieces, checking for partial matching each time. Although it is also possible to do multi-segment matching using the standard algo- rithm, by retaining partially matched substrings, it is more compli- cated. 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. REVISION Last updated: 10 October 2018 Copyright (c) 1997-2018 University of Cambridge. PCRE2 10.33 10 October 2018PCRE2MATCHING(3)