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We generalize an efficient automata-based approach to string constraint solving, the stabilization-based method behind the solver Z3-Noodler, to support relational constraints represented by finite-state transducers (useful, for example,…

Formal Languages and Automata Theory · Computer Science 2026-05-19 David Chocholatý , Vojtěch Havlena , Lukáš Holík , Juraj Síč , Michal Šedý

Z3-Noodler is a fork of Z3 that replaces its string theory solver with a custom solver implementing the recently introduced stabilization-based algorithm for solving word equations with regular constraints. An extensive experimental…

Logic in Computer Science · Computer Science 2023-10-18 Yu-Fang Chen , David Chocholatý , Vojtěch Havlena , Lukáš Holík , Ondřej Lengál , Juraj Síč

We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…

Formal Languages and Automata Theory · Computer Science 2023-07-11 Parosh Aziz Abdulla , Mohamed Faouzi Atig Bui Phi Diep , Lukáš Holík , Petr Janků

String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of cross-site scripting (XSS). A popular string analysis technique includes symbolic…

Logic in Computer Science · Computer Science 2020-11-02 Lukas Holik , Petr Janku , Anthony W. Lin , Philipp Rümmer , Tomas Vojnar

String constraint solving refers to solving combinatorial problems involving constraints over string variables. String solving approaches have become popular over the last years given the massive use of strings in different application…

Artificial Intelligence · Computer Science 2021-07-01 Roberto Amadini

When eating spaghetti, one should have the sauce and noodles mixed instead of eating them separately. We argue that also in string solving, word equations and regular constraints are better mixed together than approached separately as in…

Logic in Computer Science · Computer Science 2022-12-06 František Blahoudek , Yu-Fang Chen , David Chocholatý , Vojtěch Havlena , Lukáš Holík , Ondřej Lengál , Juraj Síč

We report (to our knowledge) the first evaluation of Constraint Satisfaction as a computational framework for solving closest string problems. We show that careful consideration of symbol occurrences can provide search heuristics that…

Artificial Intelligence · Computer Science 2010-05-04 Tom Kelsey , Lars Kotthoff

We present a novel length-aware solving algorithm for the quantifier-free first-order theory over regex membership predicate and linear arithmetic over string length. We implement and evaluate this algorithm and related heuristics in the Z3…

Logic in Computer Science · Computer Science 2021-05-10 Murphy Berzish , Mitja Kulczynski , Federico Mora , Florin Manea , Joel D. Day , Dirk Nowotka , Vijay Ganesh

Strings are widely used in programs, especially in web applications. Integer data type occurs naturally in string-manipulating programs, and is frequently used to refer to lengths of, or positions in, strings. Analysis and testing of…

Logic in Computer Science · Computer Science 2020-07-15 Taolue Chen , Matthew Hague , Jinlong He , Denghang Hu , Anthony Widjaja Lin , Philipp Rummer , Zhilin Wu

The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…

Programming Languages · Computer Science 2025-09-09 Denghang Hu , Taolue Chen , Philipp Rümmer , Fu Song , Zhilin Wu

Regular expressions are a classical concept in formal language theory. Regular expressions in programming languages (RegEx) such as JavaScript, feature non-standard semantics of operators (e.g. greedy/lazy Kleene star), as well as…

String constraint solving, and the underlying theory of word equations, are highly interesting research topics both for practitioners and theoreticians working in the wide area of satisfiability modulo theories. As string constraint solving…

Logic in Computer Science · Computer Science 2022-08-19 Joel D. Day , Adrian Kröger , Mitja Kulczynski , Florin Manea , Dirk Nowotka , Danny Bøgsted Poulsen

In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…

Logic in Computer Science · Computer Science 2016-10-12 Quang Loc Le

Theories over strings are among the most heavily researched logical theories in the SMT community in the past decade, owing to the error-prone nature of string manipulations, which often leads to security vulnerabilities (e.g. cross-site…

Programming Languages · Computer Science 2021-12-15 Shuanglong Kan , Anthony W. Lin , Philipp Rümmer , Micha Schrader

We present a new string SMT solver, Z3str3, that is faster than its competitors Z3str2, Norn, CVC4, S3, and S3P over a majority of three industrial-strength benchmarks, namely Kaluza, PISA, and IBM AppScan. Z3str3 supports string equations,…

Logic in Computer Science · Computer Science 2017-04-27 Murphy Berzish , Yunhui Zheng , Vijay Ganesh

Although Boolean Constraint Technology has made tremendous progress over the last decade, the efficacy of state-of-the-art solvers is known to vary considerably across different types of problem instances and is known to depend strongly on…

Artificial Intelligence · Computer Science 2014-01-07 Holger Hoos , Roland Kaminski , Marius Lindauer , Torsten Schaub

The past decade has witnessed substantial developments in string solving. Motivated by the complexity of string solving strategies adopted in existing string solvers, we investigate a simple and generic method for solving string…

Logic in Computer Science · Computer Science 2025-08-28 Matthew Hague , Artur Jeż , Anthony W. Lin , Oliver Markgraf , Philipp Rümmer

Recently, it was shown that any theory of strings containing the string-replace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of…

Logic in Computer Science · Computer Science 2017-11-10 Taolue Chen , Yan Chen , Matthew Hague , Anthony W. Lin , Zhilin Wu

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…

Artificial Intelligence · Computer Science 2023-11-09 Felix Ulrich-Oltean , Peter Nightingale , James Alfred Walker

Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…

Formal Languages and Automata Theory · Computer Science 2023-04-12 Tomáš Fiedor , Lukáš Holík , Martin Hruška , Adam Rogalewicz , Juraj Síč , Pavol Vargovčík
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