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Related papers: Reachability in Two-Dimensional Vector Addition Sy…

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We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems…

Formal Languages and Automata Theory · Computer Science 2015-07-28 Jérôme Leroux , Grégoire Sutre , Patrick Totzke

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

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

We study the complexity of the reachability problem for Vector Addition Systems with States (VASSes) in fixed dimensions. We provide four lower bounds improving the currently known state-of-the-art: 1) \np-hardness for unary flat $4$-VASSes…

Formal Languages and Automata Theory · Computer Science 2022-03-09 Wojciech Czerwiński , Łukasz Orlikowski

Vector addition systems with states (VASS) are a popular model for concurrent systems. However, many decision problems have prohibitively high complexity. Therefore, it is sometimes useful to consider overapproximating semantics in which…

Logic in Computer Science · Computer Science 2023-09-14 Pascal Baumann , Khushraj Madnani , Filip Mazowiecki , Georg Zetzsche

Reachability of vector addition systems with states (VASS) is Ackermann complete~\cite{leroux2021reachability,czerwinski2021reachability}. For $d$-dimensional VASS reachability it is known that the problem is…

Computational Complexity · Computer Science 2025-04-18 Yuxi Fu , Yangluo Zheng , Qizhe Yang

Vector Addition Systems and equivalent Petri nets are a well established models of concurrency. The central algorithmic problem for Vector Addition Systems with a long research history is the reachability problem asking whether there exists…

Formal Languages and Automata Theory · Computer Science 2022-10-27 Wojciech Czerwiński , Łukasz Orlikowski

A complete characterization of the complexity of the reachability problem for vector addition system has been open for a long time. The problem is shown to be Tower complete.

Logic in Computer Science · Computer Science 2020-03-24 Yuxi Fu , Qizhe Yang

The recent years have seen remarkable progress in establishing the complexity of the reachability problem for vector addition systems with states (VASS), equivalently known as Petri nets. Existing work primarily considers the case in which…

Formal Languages and Automata Theory · Computer Science 2023-10-26 Andrei Draghici , Christoph Haase , Andrew Ryzhikov

The reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known to be decidable by algorithms exclusively based on the classical Kosaraju-Lambert-Mayr-Sacerdote-Tenney…

Logic in Computer Science · Computer Science 2015-07-01 leroux jerome

The reachability problem for vector addition systems with states (VASS) has been shown to be \textsc{Ackermann}-complete. For every $k\geq 3$, a completeness result for the $k$-dimensional VASS reachability problem is not yet available. It…

Formal Languages and Automata Theory · Computer Science 2023-08-22 Qizhe Yang , Yuxi Fu

Does the trace language of a given vector addition system (VAS) intersect with a given context-free language? This question lies at the heart of several verification questions involving recursive programs with integer parameters. In…

Formal Languages and Automata Theory · Computer Science 2015-04-30 Jérôme Leroux , Grégoire Sutre , Patrick Totzke

The geometric dimension $g$ of a Vector Addition System with States (VASS) is the dimension of the vector space generated by cycles in the VASS; this parameter refines the standard dimension $d$, the number of counters. Recently, it was…

Formal Languages and Automata Theory · Computer Science 2026-02-18 Wojciech Czerwiński , Roland Guttenberg , Łukasz Orlikowski , Henry Sinclair-Banks , Yangluo Zheng

Reachability problems in infinite-state systems are often subject to extremely high complexity. This motivates the investigation of efficient overapproximations, where we add transitions to obtain a system in which reachability can be…

Formal Languages and Automata Theory · Computer Science 2022-06-28 Moses Ganardi , Rupak Majumdar , Georg Zetzsche

We consider a variant of reachability in Vector Addition Systems (VAS) dubbed \emph{box reachability}, whereby a vector $v\in \mathbb{N}^d$ is box-reachable from $0$ in a VAS $V$ if $V$ admits a path from $0$ to $v$ that not only stays in…

Formal Languages and Automata Theory · Computer Science 2025-08-19 Shaull Almagor , Itay Hasson , Michał Pilipczuk , Michael Zaslavski

We consider a variant of VASS extended with integer counters, denoted VASS+Z. These are automata equipped with N and Z counters; the N-counters are required to remain nonnegative and the Z-counters do not have this restriction. We study the…

Formal Languages and Automata Theory · Computer Science 2026-03-06 Clotilde Bizière , Wojciech Czerwiński , Roland Guttenberg , Jérôme Leroux , Vincent Michielini , Łukasz Orlikowski , Antoni Puch , Henry Sinclair-Banks

We consider the model of pushdown vector addition systems with resets. These consist of vector addition systems that have access to a pushdown stack and have instructions to reset counters. For this model, we study the coverability problem.…

Formal Languages and Automata Theory · Computer Science 2022-05-12 Sylvain Schmitz , Georg Zetzsche

Vector Addition Systems (VAS), aka Petri nets, are a popular model of concurrency. The reachability set of a VAS is the set of configurations reachable from the initial configuration. Leroux has studied the geometric properties of VAS…

Formal Languages and Automata Theory · Computer Science 2023-07-25 Roland Guttenberg , Mikhail Raskin , Javier Esparza

We consider two-player turn-based games with zero-reachability and zero-safety objectives generated by extended vector addition systems with states. Although the problem of deciding the winner in such games is undecidable in general, we…

Computer Science and Game Theory · Computer Science 2010-02-15 Tomas Brazdil , Petr Jancar , Antonin Kucera

We investigate the reachability problem in symmetric vector addition systems with states (VASS), where transitions are invariant under a group of permutations of coordinates. One extremal case, the trivial groups, yields general VASS. In…

Formal Languages and Automata Theory · Computer Science 2026-01-12 Łukasz Kamiński , Sławomir Lasota