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ReDoS is a well-known type of algorithmic complexity attack, where an adversary supplies maliciously crafted strings to a regular expression matching engine, aiming to exhaust computational resources of systems. Even quadratic-time behavior…

Data Structures and Algorithms · Computer Science 2026-05-11 Soh Kumabe , Yuya Uezato

Backreference is a well-known practical extension of regular expressions and most modern programming languages, such as Java, Python, JavaScript and more, support regular expressions with backreferences (rewb) in their standard libraries…

Formal Languages and Automata Theory · Computer Science 2024-06-28 Taisei Nogami , Tachio Terauchi

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…

Programming Languages · Computer Science 2024-02-02 Hiroya Fujinami , Ichiro Hasuo

A rewb is a regular expression extended with a feature called backreference. It is broadly known that backreference is a practical extension of regular expressions, and is supported by most modern regular expression engines, such as those…

Formal Languages and Automata Theory · Computer Science 2025-07-23 Taisei Nogami , Tachio Terauchi

Regular expressions with backreferences (regex, for short), as supported by most modern libraries for regular expression matching, have an NP-complete matching problem. We define a complexity parameter of regex, called active variable…

Formal Languages and Automata Theory · Computer Science 2024-02-09 Markus L. Schmid

Matching regexes (regular expressions) is a common problem in many areas of computer science, with requirements on high speed and robust performance. Regexes with backreferences allow one to express certain patterns (even beyond regular)…

Logic in Computer Science · Computer Science 2026-04-16 Vojtěch Havlena , Lukáš Holík , Ondřej Lengál , Jan Vašák , Sabína Gulčíková

Regularization of neural machine translation is still a significant problem, especially in low-resource settings. To mollify this problem, we propose regressing word embeddings (ReWE) as a new regularization technique in a system that is…

Computation and Language · Computer Science 2019-04-05 Inigo Jauregi Unanue , Ehsan Zare Borzeshi , Nazanin Esmaili , Massimo Piccardi

In this paper we revisit the classical regular expression matching problem, namely, given a regular expression $R$ and a string $Q$, decide if $Q$ matches one of the strings specified by $R$. Let $m$ and $n$ be the length of $R$ and $Q$,…

Data Structures and Algorithms · Computer Science 2007-05-23 Philip Bille

The regular expression matching problem asks whether a given regular expression of length $m$ matches a given string of length $n$. As is well known, the problem can be solved in $O(nm)$ time using Thompson's algorithm. Moreover, recent…

Computational Complexity · Computer Science 2026-04-03 Taisei Nogami , Yoshiki Nakamura , Tachio Terauchi

Modern regex languages have strayed far from well-understood traditional regular expressions: they include features that fundamentally transform the matching problem. In exchange for these features, modern regex engines at times suffer from…

Programming Languages · Computer Science 2024-07-24 Aurèle Barrière , Clément Pit-Claudel

Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular…

Data Structures and Algorithms · Computer Science 2019-01-30 Philip Bille , Inge Li Gørtz

An extended regular expression $R$ specifies a set of strings formed by characters from an alphabet combined with concatenation, union, intersection, complement, and star operators. Given an extended regular expression $R$ and a string $Q$,…

Data Structures and Algorithms · Computer Science 2026-02-09 Philip Bille , Inge Li Gørtz , Rikke Schjeldrup Jessen

Existing support for regular expressions in automated test generation or verification tools is lacking. Common aspects of regular expression engines found in mainstream programming languages, such as backreferences or greedy matching, are…

Programming Languages · Computer Science 2020-03-16 Blake Loring , Duncan Mitchell , Johannes Kinder

Regular expressions constitute a fundamental notion in formal language theory and are frequently used in computer science to define search patterns. A classic algorithm for these problems constructs and simulates a non-deterministic finite…

Computational Complexity · Computer Science 2016-09-28 Arturs Backurs , Piotr Indyk

We present a tool and theory RE# for regular expression matching that is built on symbolic derivatives, does not use backtracking, and, in addition to the classical operators, also supports complement, intersection and lookarounds. We…

Formal Languages and Automata Theory · Computer Science 2025-01-27 Ian Erik Varatalu , Margus Veanes , Juhan-Peep Ernits

In recent years, neural machine translation (NMT) has become the dominant approach in automated translation. However, like many other deep learning approaches, NMT suffers from overfitting when the amount of training data is limited. This…

Computation and Language · Computer Science 2019-10-01 Inigo Jauregi Unanue , Ehsan Zare Borzeshi , Massimo Piccardi

Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…

Formal Languages and Automata Theory · Computer Science 2023-01-31 Lukáš Holík , Juraj Síč , Lenka Turoňová , Tomáš Vojnar

We present the first mechanized, succinct, practical, complete, and proven-faithful semantics for a modern regular expression language with backtracking semantics. We ensure its faithfulness by proving it equivalent to a preexisting…

Programming Languages · Computer Science 2026-04-08 Aurèle Barrière , Victor Deng , Clément Pit-Claudel

We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmic-sized…

Data Structures and Algorithms · Computer Science 2008-09-22 Philip Bille , Martin Farach-Colton

This paper is devoted to finite state automata, regular expression matching, pattern recognition, and the exponential blow-up problem, which is the growing complexity of automata exponentially depending on regular expression length. This…

Formal Languages and Automata Theory · Computer Science 2023-08-22 Alexandra Bernadotte
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