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We study a class of reachability problems in weighted graphs with constraints on the accumulated weight of paths. The problems we study can equivalently be formulated in the model of vector addition systems with states (VASS). We consider a…

Logic in Computer Science · Computer Science 2020-09-08 Shaull Almagor , Nathann Cohen , Guillermo A. Pérez , Mahsa Shirmohammadi , James Worrell

The reachability problem in vector addition systems is a central question, not only for the static verification of these systems, but also for many inter-reducible decision problems occurring in various fields. The currently best known…

Logic in Computer Science · Computer Science 2019-08-20 Jérôme Leroux , Sylvain Schmitz

An $\mathsf{F}_{d}$ upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where $\mathsf{F}_d$ is the $d$-th level of the Grzegorczyk hierarchy of complexity classes. The new…

Logic in Computer Science · Computer Science 2024-04-24 Yuxi Fu , Qizhe Yang , Yangluo Zheng

By adapting the iterative yardstick construction of Stockmeyer, we show that the reachability problem for vector addition systems with a stack does not have elementary complexity. As a corollary, the same lower bound holds for the…

Formal Languages and Automata Theory · Computer Science 2013-10-08 Ranko Lazic

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

We design a variation of the Karp-Miller algorithm to compute, in a forward manner, a finite representation of the cover (i.e., the downward closure of the reachability set) of a vector addition system with one zero-test. This algorithm…

Discrete Mathematics · Computer Science 2015-07-01 Rémi Bonnet , Alain FInkel , Jérôme Leroux , Marc Zeitoun

In this paper we consider the reachability problem for bounded branching VASS. Bounded VASS are a variant of the classic VASS model where all values in all configurations are upper bounded by a fixed natural number, encoded in binary in the…

Formal Languages and Automata Theory · Computer Science 2019-08-20 Filip Mazowiecki , Michał Pilipczuk

A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and…

Formal Languages and Automata Theory · Computer Science 2020-07-20 Krishnendu Chatterjee , Thomas A. Henzinger , Jan Otop

We study the reachability problem for affine $\mathbb{Z}$-VASS, which are integer vector addition systems with states in which transitions perform affine transformations on the counters. This problem is easily seen to be undecidable in…

Logic in Computer Science · Computer Science 2023-06-22 Michael Blondin , Christoph Haase , Filip Mazowiecki , Mikhail Raskin

This note is a product of digestion of the famous proof of decidability of the reachability problem for vector addition systems with states (VASS), as first established by Mayr in 1981 and then simplified by Kosaraju in 1982. The note is…

Logic in Computer Science · Computer Science 2020-05-28 Sławomir Lasota

In many kinds of infinite-state systems, the coverability problem has significantly lower complexity than the reachability problem. In order to delineate the border of computational hardness between coverability and reachability, we propose…

Formal Languages and Automata Theory · Computer Science 2025-05-21 Yousef Shakiba , Henry Sinclair-Banks , Georg Zetzsche

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

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

Vector addition systems are an important model in theoretical computer science and have been used in a variety of areas. In this paper, we consider vector addition systems with states over a parameterized initial configuration. For these…

Formal Languages and Automata Theory · Computer Science 2020-03-17 Florian Zuleger

We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et…

Computational Complexity · Computer Science 2020-07-03 Stefan Jaax , Stefan Kiefer

A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left…

Formal Languages and Automata Theory · Computer Science 2019-05-15 Krishnendu Chatterjee , Thomas A. Henzinger , Jan Otop

Coverability in Petri nets finds applications in verification of safety properties of reactive systems. We study coverability in the equivalent model: Vector Addition Systems with States (VASS). A k-VASS can be seen as k counters and a…

Formal Languages and Automata Theory · Computer Science 2023-02-01 Filip Mazowiecki , Henry Sinclair-Banks , Karol Węgrzycki

Vector addition systems (VAS), also known as Petri nets, are a popular model of concurrent systems. Many problems from many areas reduce to the reachability problem for VAS, which consists of deciding whether a target configuration of a VAS…

Formal Languages and Automata Theory · Computer Science 2024-05-01 Roland Guttenberg

This paper is about reachability analysis in a restricted subclass of multi-pushdown automata. We assume that the control states of an automaton are partially ordered, and all transitions of an automaton go downwards with respect to the…

Logic in Computer Science · Computer Science 2015-07-01 Wojciech Czerwiński , Piotr Hofman , SŁawomir Lasota

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