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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

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 study the geometry of reachability sets of continuous vector addition systems with states (VASS). In particular we establish that they are almost Minkowski sums of convex cones and zonotopes generated by the vectors labelling the…

Logic in Computer Science · Computer Science 2022-11-15 Shaull Almagor , Arka Ghosh , Tim Leys , Guillermo A. Perez

This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…

Logic in Computer Science · Computer Science 2011-06-08 Olga Tveretina , Daniel Funke

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

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

In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging…

Systems and Control · Electrical Eng. & Systems 2021-09-21 Yiliang Li , Haitao Li , Jun-e Feng , Jinjin Li

Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is the verification of safety and liveness properties in this model; despite the…

Logic in Computer Science · Computer Science 2016-08-09 Petr Jancar

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

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

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

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

Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary…

Logic in Computer Science · Computer Science 2020-10-16 Michael Blondin , Christoph Haase , Philip Offtermatt

A central decision problem in Petri net theory is reachability asking whether a given marking can be reached from the initial marking. Related is the covering problem (or sub-marking reachbility), which decides whether there is a reachable…

Formal Languages and Automata Theory · Computer Science 2026-02-03 Thomas M. Prinz , Christopher T. Schwanen , Wil M. P. van der Aalst

Dynamic networks of concurrent pushdown systems (DCPS) are a theoretical model for multi-threaded recursive programs with shared global state and dynamical creation of threads. The (global) state reachability problem for DCPS is undecidable…

Formal Languages and Automata Theory · Computer Science 2020-11-19 Pascal Baumann , Rupak Majumdar , Ramanathan S. Thinniyam , Georg Zetzsche

Blondin et al. showed at LICS 2015 that two-dimensional vector addition systems with states have reachability witnesses of length exponential in the number of states and polynomial in the norm of vectors. The resulting guess-and-verify…

Logic in Computer Science · Computer Science 2016-05-09 Matthias Englert , Ranko Lazić , Patrick Totzke

We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…

Optimization and Control · Mathematics 2021-03-16 Mohan Dantam , Amaury Pouly

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 propose a new pumping technique for 2-dimensional vector addition systems with states (2-VASS) building on natural geometric properties of runs. We illustrate its applicability by reproving an exponential bound on the length of the…

Formal Languages and Automata Theory · Computer Science 2019-06-26 Wojciech Czerwiński , Sławomir Lasota , Christof Löding , Radosław Piórkowski

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