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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

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

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

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

This paper presents the reachability analysis of curves in $\mathbb{R}^3$ with a prescribed curvature bound. Based on Pontryagin Maximum Principle, we leverage the existing knowledge on the structure of solutions to minimum-time problems,…

Optimization and Control · Mathematics 2025-03-27 Juho Bae , Ji Hoon Bai , Byung-Yoon Lee , Jun-Yong Lee , Chang-Hun Lee

We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…

Computational Geometry · Computer Science 2019-03-12 Irina Kostitsyna , Maarten Löffler , Valentin Polishchuk , Frank Staals

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

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 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

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

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

Seminal results establish that the coverability problem for Vector Addition Systems with States (VASS) is in EXPSPACE (Rackoff, '78) and is EXPSPACE-hard already under unary encodings (Lipton, '76). More precisely, Rosier and Yen later…

Formal Languages and Automata Theory · Computer Science 2023-05-03 Marvin Künnemann , Filip Mazowiecki , Lia Schütze , 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

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business…

Formal Languages and Automata Theory · Computer Science 2019-04-12 Wojciech Czerwinski , Slawomir Lasota , Ranko Lazic , Jerome Leroux , Filip Mazowiecki

The decision problems on matrices were intensively studied for many decades as matrix products play an essential role in the representation of various computational processes. However, many computational problems for matrix semigroups are…

Formal Languages and Automata Theory · Computer Science 2016-04-28 Igor Potapov , Pavel Semukhin

This paper presents a reachability-based approach to finite-time transition problem of nonlinear systems between two stationary points (i.e., the point-to-point steering problem). When the target state is reachable, we prove that a solution…

Optimization and Control · Mathematics 2025-09-23 Juho Bae , Han-Lim Choi

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

Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem. Therefore, there have been several proposals to underapproximate their sets of runs so that reachability in…

Formal Languages and Automata Theory · Computer Science 2021-08-03 Aneesh K. Shetty , S. Krishna , Georg Zetzsche

The reachability problem in cooperating systems is known to be PSPACE-complete. We show here that this problem remains PSPACE-complete when we restrict the communication structure between the subsystems in various ways. For this purpose we…

Computational Complexity · Computer Science 2013-12-31 Mila Majster-Cederbaum , Nils Semmelrock

We study the complexity of reachability problems on branching extensions of vector addition systems, which allows us to derive new non-elementary complexity bounds for fragments and variants of propositional linear logic. We show that…

Logic in Computer Science · Computer Science 2022-05-18 Ranko Lazić , Sylvain Schmitz