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A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable…

Formal Languages and Automata Theory · Computer Science 2015-07-01 Thomas Place , Lorijn van Rooijen , Marc Zeitoun

Reachability in pushdown vector addition systems with states (PVASS) is among the longest standing open problems in Theoretical Computer Science. We show that the problem is decidable in full generality. Our decision procedure is similar in…

Logic in Computer Science · Computer Science 2026-02-19 Roland Guttenberg , Eren Keskin , Roland Meyer

We study languages of unambiguous VASS, that is, Vector Addition Systems with States, whose transitions read letters from a finite alphabet, and whose acceptance condition is defined by a set of final states (i.e., the coverability…

Formal Languages and Automata Theory · Computer Science 2020-07-22 Wojciech Czerwiński , Diego Figueira , Piotr Hofman

We investigate the parameterised complexity of the classic coverability problem for vector addition systems (VAS): given a finite set of vectors $V \subseteq\mathbb{Z}^d$, an initial configuration $s\in\mathbb{N}^d$, and a target…

Computational Complexity · Computer Science 2025-12-16 Michał Pilipczuk , Sylvain Schmitz , Henry Sinclair-Banks

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…

Formal Languages and Automata Theory · Computer Science 2013-04-26 Thomas Place , Lorijn van Rooijen , Marc Zeitoun

Vectors addition systems with states (VASS), or equivalently Petri nets, are arguably one of the most studied formalisms for the modeling and analysis of concurrent systems. A central decision problem for VASS is reachability: whether there…

Logic in Computer Science · Computer Science 2025-07-01 Clotilde Bizière , Thibault Hilaire , Jérôme Leroux , Grégoire Sutre

Vector addition system with states (VASS) is a popular model for the verification of concurrent systems. VASS consists of finitely many control states and a set of counters which can be incremented and decremented, but not tested for zero.…

Logic in Computer Science · Computer Science 2024-05-21 A. R. Balasubramanian

Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem…

Formal Languages and Automata Theory · Computer Science 2013-03-12 Lorijn van Rooijen , Marc Zeitoun

The following problem is shown undecidable: given regular languages L,K of finite trees, decide if there exists a deterministic tree-walking automaton which accepts all trees in L and rejects all trees in K. The proof uses a technique of…

Logic in Computer Science · Computer Science 2017-03-21 Mikołaj Bojańczyk

Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…

Formal Languages and Automata Theory · Computer Science 2023-05-01 Thomas Place , Marc Zeitoun

More than 30 years after their inception, the decidability proofs for reachability in vector addition systems (VAS) still retain much of their mystery. These proofs rely crucially on a decomposition of runs successively refined by Mayr,…

Logic in Computer Science · Computer Science 2015-08-11 Jérôme Leroux , Sylvain Schmitz

A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown stack. The algorithmic analysis of PVASS has applications such as static analysis of recursive programs manipulating integer…

Logic in Computer Science · Computer Science 2024-02-21 Guillermo A. Perez , Shrisha Rao

We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…

Formal Languages and Automata Theory · Computer Science 2025-02-03 Corentin Barloy , Michaël Cadilhac , Charles Paperman , Howard Straubing

Determining the complexity of the reachability problem for vector addition systems with states (VASS) is a long-standing open problem in computer science. Long known to be decidable, the problem to this day lacks any complexity upper bound…

Formal Languages and Automata Theory · Computer Science 2017-03-20 Michael Blondin , Alain Finkel , Stefan Göller , Christoph Haase , Pierre McKenzie

Vector addition systems (VAS) constitute an important model of computation and concurrency that is equally expressive as the Petri net model. Recently, a lot of research has been conducted on vector addition systems with states (VASS),…

Formal Languages and Automata Theory · Computer Science 2026-04-28 Weijun Chen , Yuxi Fu , Yangluo Zheng

This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finite-state controller with a finite number of…

Formal Languages and Automata Theory · Computer Science 2014-10-01 Christoph Haase , Simon Halfon

Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is…

Formal Languages and Automata Theory · Computer Science 2023-11-01 A. R. Balasubramanian , Rupak Majumdar , Ramanathan S. Thinniyam , Georg Zetzsche

We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…

Formal Languages and Automata Theory · Computer Science 2015-01-06 Thomas Place , Marc Zeitoun

Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…

Formal Languages and Automata Theory · Computer Science 2017-01-11 Thomas Place , Marc Zeitoun

Despite recent progress which settled the complexity of the reachability problem for Vector Addition Systems with States (VASSes) as being Ackermann-complete we still lack much understanding for that problem. A striking example is the…

Formal Languages and Automata Theory · Computer Science 2022-09-14 Wojciech Czerwiński , Adam Jędrych