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We consider the model of one-dimensional Pushdown Vector Addition Systems (1-PVAS), a fundamental computational model simulating both recursive and concurrent behaviours. Our main result is decidability of the reachability problem for…

Formal Languages and Automata Theory · Computer Science 2024-11-05 Clotilde Bizière , Wojciech Czerwiński

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

A control system consists of a plant component and a controller which periodically computes a control input for the plant. We consider systems where the controller is implemented by a feedforward neural network with ReLU activations. The…

Machine Learning · Computer Science 2024-12-10 Christian Schilling , Martin Zimmermann

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 conjunctive…

Computational Complexity · Computer Science 2022-03-16 Marco Sälzer , Martin Lange

We consider the reachability problem on transition systems corresponding to succinct one-counter machines, that is, machines where the counter is incremented or decremented by a value given in binary.

Logic in Computer Science · Computer Science 2014-07-21 Paul Hunter

We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability…

Logic in Computer Science · Computer Science 2014-01-27 Yangjia Li , Mingsheng Ying

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 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

When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…

Optimization and Control · Mathematics 2014-01-23 Kendra Lesser , Meeko Oishi

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes…

Systems and Control · Computer Science 2014-03-06 Oded Maler

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

A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown stack. The algorithmic analysis of PVASS has applications such as static analysis of recursive programs manipulating integer…

Logic in Computer Science · Computer Science 2024-02-21 Guillermo A. Perez , Shrisha Rao

A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown store. A PVASS is said to be \emph{bidirected} if every transition (pushing/popping a symbol or modifying a counter) has an…

Formal Languages and Automata Theory · Computer Science 2022-04-26 Moses Ganardi , Rupak Majumdar , Andreas Pavlogiannis , Lia Schütze , Georg Zetzsche

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 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

In this paper we investigate formal verification problems for Neural Network computations. Various reachability problems will be in the focus, such as: Given symbolic specifications of allowed inputs and outputs in form of Linear…

Computational Complexity · Computer Science 2023-06-12 Adrian Wurm

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

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

A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs…

Formal Languages and Automata Theory · Computer Science 2022-01-14 Evgeniya A. Bondar , David Casas , Mikhail V. Volkov

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