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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

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

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

Petri nets, equivalently presentable as vector addition systems with states, are an established model of concurrency with widespread applications. The reachability problem, where we ask whether from a given initial configuration there…

Formal Languages and Automata Theory · Computer Science 2022-01-14 Sławomir Lasota

We provide an Ackermannian complexity lower bound for the reachability problem for checking programs, a model equivalent to Petri nets. Moreover in fixed dimension $2d+4$, we show that the problem is $\mathbb{F}_d$-hard. As a direct…

Logic in Computer Science · Computer Science 2021-09-03 Jérôme Leroux

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

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

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 investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…

Computational Complexity · Computer Science 2026-04-08 Marco Sälzer , Martin Lange

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

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

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

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

In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…

Data Structures and Algorithms · Computer Science 2012-06-26 Allen Chang , Eyal Amir

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

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

We investigate Petri nets with data, an extension of plain Petri nets where tokens carry values from an infinite data domain, and executability of transitions is conditioned by equalities between data values. We provide a decision procedure…

Computation and Language · Computer Science 2024-07-12 Łukasz Kamiński , 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

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