Regular Expressions with Lookahead

Berglund, Martin; Merwe, Brink van der; Litsenborgh, Steyn van

doi:10.3897/jucs.66330

Cited by 6 publications

(3 citation statements)

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“…Additionally, the diagram below summarizes the results of the hierarchy of the language classes. Here, L L denotes the class of languages matched by regular expressions with (both positive and negative) lookaheads, which is known to be equivalent in expressive power to the set of regular languages [4], [5]. From Theorems 1 and 2, we also obtain the following result.…”

Section: Theorem 2 L Bl Is Closed Under Union Intersection and Comple...mentioning

confidence: 96%

“…Previous works on formal language theory have studied the two features mostly in isolation. Morihata [4] and Berglund et al [5] showed that extending regular ex-pressions by lookaheads does not enhance their expressive power. Their proofs are by a translation to boolean finite automata [6] whose expressive power is regular.…”

Section: Introductionmentioning

confidence: 99%

“…Another consequence of our results is that neither the class of finite state automata nor that of memory automata (MFA) of Schmid [2] (which corresponds to regular expressions with backreferences but without lookaheads) corresponds to rewbl p or rewbl n . As remarked above, prior works [4], [5] have applied translation to boolean finite automata [6] (or alternating finite automata [11]) to build automata equivalent to regular expressions with lookaheads. They simulate lookaheads by executing multiple runs simultaneously without backtracking.…”

Section: Introductionmentioning

confidence: 99%

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On Lookaheads in Regular Expressions with Backreferences

Chida

Terauchi

2023

IEICE Trans. Inf. & Syst.

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Many modern regular expression engines employ various extensions to give more expressive support for real-world usages. Among the major extensions employed by many of the modern regular expression engines are backreferences and lookaheads. A question of interest about these extended regular expressions is their expressive power. Previous works have shown that (i) the extension by lookaheads does not enhance the expressive power, i.e., the expressive power of regular expressions with lookaheads is still regular, and that (ii) the extension by backreferences enhances the expressive power, i.e., the expressive power of regular expressions with backreferences (abbreviated as rewb) is no longer regular. This raises the following natural question: Does the extension of regular expressions with backreferences by lookaheads enhance the expressive power of regular expressions with backreferences? This paper answers the question positively by proving that adding either positive lookaheads or negative lookaheads increases the expressive power of rewb (the former abbreviated as rewbl p and the latter as rewbl n ). A consequence of our result is that neither the class of finite state automata nor that of memory automata (MFA) of Schmid [2] (which corresponds to regular expressions with backreferenes but without lookaheads) corresponds to rewbl p or rewbl n . To fill the void, as a first step toward building such automata, we propose a new class of automata called memory automata with positive lookaheads (PLMFA) that corresponds to rewbl p . The key idea of PLMFA is to extend MFA with a new kind of memories, called positive-lookahead memory, that is used to simulate the backtracking behavior of positive lookaheads. Interestingly, our positive-lookahead memories are almost perfectly symmetric to the capturing-group memories of MFA. Therefore, our PLMFA can be seen as a natural extension of MFA that can be obtained independently of its original intended purpose of simulating rewbl p .

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Section: Theorem 2 L Bl Is Closed Under Union Intersection and Comple...mentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Lookaheads in Regular Expressions with Backreferences

Chida

Terauchi

2023

IEICE Trans. Inf. & Syst.

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Efficient Matching with Memoization for Regexes with Look-around and Atomic Grouping

Fujinami,

Hasuo

2024

Lecture Notes in Computer Science

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Regular expression (regex) matching is fundamental in many applications, especially in web services. However, matching by backtracking—preferred by most real-world implementations for its practical performance and backward compatibility—can suffer from so-called catastrophic backtracking, which makes the number of backtracking super-linear and leads to the well-known ReDoS vulnerability. Inspired by a recent algorithm by Davis et al. that runs in linear time for (non-extended) regexes, we study efficient backtracking matching for regexes with two common extensions, namely look-around and atomic grouping. We present linear-time backtracking matching algorithms for these extended regexes. Their efficiency relies on memoization, much like the one by Davis et al.; we also strive for smaller memoization tables by carefully trimming their range. Our experiments—we used some real-world regexes with the aforementioned extensions—confirm the performance advantage of our algorithms.

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