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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

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

Regular expression matching is essential for many applications, such as finding patterns in text, exploring substrings in large DNA sequences, or lexical analysis. However, sequential regular expression matching may be time-prohibitive for…

Formal Languages and Automata Theory · Computer Science 2015-06-30 Suejb Memeti , Sabri Pllana

A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…

Formal Languages and Automata Theory · Computer Science 2022-07-13 Marek Szykuła , Adam Zyzik

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

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

In this paper, we present a fast and strong neural approach for general purpose text matching applications. We explore what is sufficient to build a fast and well-performed text matching model and propose to keep three key features…

Computation and Language · Computer Science 2019-08-02 Runqi Yang , Jianhai Zhang , Xing Gao , Feng Ji , Haiqing Chen

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

We develop a formal perspective on how regular expression matching works in Java, a popular representative of the category of regex-directed matching engines. In particular, we define an automata model which captures all the aspects needed…

Formal Languages and Automata Theory · Computer Science 2014-05-23 Martin Berglund , Frank Drewes , Brink van der Merwe

We present an algorithm for searching regular expression matches in compressed text. The algorithm reports the number of matching lines in the uncompressed text in time linear in the size of its compressed version. We define efficient data…

Formal Languages and Automata Theory · Computer Science 2019-01-17 Pierre Ganty , Pedro Valero

In this paper we present a new problem, the fast set intersection problem, which is to preprocess a collection of sets in order to efficiently report the intersection of any two sets in the collection. In addition we suggest new solutions…

Data Structures and Algorithms · Computer Science 2010-03-12 Hagai Cohen , Ely Porat

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

In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…

Data Structures and Algorithms · Computer Science 2013-09-19 Pritom Ahmed , Costas S. Iliopoulos , A. S. M. Sohidull Islam , M. Sohel Rahman

Efficient pattern matching is fundamental for practical term rewrite engines. By preprocessing the given patterns into a finite deterministic automaton the matching patterns can be decided in a single traversal of the relevant parts of the…

Logic in Computer Science · Computer Science 2023-06-22 Rick Erkens , Maurice Laveaux

This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…

Data Structures and Algorithms · Computer Science 2010-12-14 Simone Faro , Thierry Lecroq

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 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

String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal…

Data Structures and Algorithms · Computer Science 2023-03-13 Thierry Lecroq

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

Data Structures and Algorithms · Computer Science 2022-07-01 Anas Al-okaily , Abdelghani Tbakhi

String matching is the problem of finding all the substrings of a text which match a given pattern. It is one of the most investigated problems in computer science, mainly due to its very diverse applications in several fields. Recently,…

Data Structures and Algorithms · Computer Science 2017-07-04 Domenico Cantone , Simone Faro , Arianna Pavone
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