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Regular expression matching is of practical importance due to its widespread use in real-world applications. In practical use, regular expressions are often used with real-world extensions. Accordingly, the matching problem of regular…

Formal Languages and Automata Theory · Computer Science 2025-07-03 Taisei Nogami , Tachio Terauchi

Regular Expression Denial of Service (ReDoS) is a vulnerability class that has become prominent in recent years. Attackers can weaponize such weaknesses as part of asymmetric cyberattacks that exploit the slow worst-case matching time of…

Cryptography and Security · Computer Science 2025-08-27 Masudul Hasan Masud Bhuiyan , Berk Çakar , Ethan H. Burmane , James C. Davis , Cristian-Alexandru Staicu

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

In an algorithmic complexity attack, a malicious party takes advantage of the worst-case behavior of an algorithm to cause denial-of-service. A prominent algorithmic complexity attack is regular expression denial-of-service (ReDoS), in…

Cryptography and Security · Computer Science 2017-01-17 Valentin Wüstholz , Oswaldo Olivo , Marijn J. H. Heule , Isil Dillig

Regular expressions are used for diverse purposes, including input validation and firewalls. Unfortunately, they can also lead to a security vulnerability called ReDoS (Regular Expression Denial of Service), caused by a super-linear…

Software Engineering · Computer Science 2022-12-16 Sk Adnan Hassan , Zainab Aamir , Dongyoon Lee , James C. Davis , Francisco Servant

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

There has been much work on synthesizing and repairing regular expressions (regexes for short) from examples. These programming-by-example (PBE) methods help the users write regexes by letting them reflect their intention by examples.…

Programming Languages · Computer Science 2022-08-23 Nariyoshi Chida , Tachio Terauchi

Regular expression matching using backtracking can have exponential runtime, leading to an algorithmic complexity attack known as REDoS in the systems security literature. In this paper, we build on a recently published static analysis that…

Programming Languages · Computer Science 2017-08-15 Asiri Rathnayake , Hayo Thielecke

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

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

Regular expressions (regexes) are a powerful mechanism for solving string-matching problems. They are supported by all modern programming languages, and have been estimated to appear in more than a third of Python and JavaScript projects.…

Software Engineering · Computer Science 2023-03-07 Louis G. Michael , James Donohue , James C. Davis , Dongyoon Lee , Francisco Servant

It is well-known that checking whether a given string $w$ matches a given regular expression $r$ can be done in quadratic time $O(|w|\cdot |r|)$ and that this cannot be improved to a truly subquadratic running time of $O((|w|\cdot…

Data Structures and Algorithms · Computer Science 2025-08-21 Antoine Amarilli , Florin Manea , Tina Ringleb , Markus L. Schmid

Regular expressions are pervasive in modern systems. Many real-world regular expressions are inefficient, sometimes to the extent that they are vulnerable to complexity-based attacks, and while much research has focused on detecting…

Programming Languages · Computer Science 2022-09-30 Jedidiah McClurg , Miles Claver , Jackson Garner , Jake Vossen , Jordan Schmerge , Mehmet E. Belviranli

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

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

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

We study regular expression membership testing: Given a regular expression of size $m$ and a string of size $n$, decide whether the string is in the language described by the regular expression. Its classic $O(nm)$ algorithm is one of the…

Data Structures and Algorithms · Computer Science 2016-11-08 Karl Bringmann , Allan Grønlund , Kasper Green Larsen

A regular expression specifies a set of strings formed by single characters combined with concatenation, union, and Kleene star operators. Given a regular expression $R$ and a string $Q$, the regular expression matching problem is to decide…

Data Structures and Algorithms · Computer Science 2023-11-07 Philip Bille , Inge Li Gørtz

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

This paper presents the first systematic study of denial-of-service vulnerabilities in Regular Expressions with Backreferences (REwB). We introduce the Two-Phase Memory Automaton (2PMFA), an automaton model that precisely captures REwB…

Cryptography and Security · Computer Science 2026-02-26 Yichen Liu , Berk Çakar , Aman Agrawal , Minseok Seo , James C. Davis , Dongyoon Lee
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