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Related papers: Reachability in 3-VASS is Elementary

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We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…

In extension problems of partial graph drawings one is given an incomplete drawing of an input graph $G$ and is asked to complete the drawing while maintaining certain properties. A prominent area where such problems arise is that of…

Computational Geometry · Computer Science 2020-12-15 Robert Ganian , Thekla Hamm , Fabian Klute , Irene Parada , Birgit Vogtenhuber

Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using…

Formal Languages and Automata Theory · Computer Science 2010-11-02 Stéphane Demri

This manuscript presents an innovative framework for constructing barrier functions to bound reachability probabilities for continuous-time stochastic systems described by stochastic differential equations (SDEs). The reachability…

Systems and Control · Electrical Eng. & Systems 2025-12-09 Bai Xue

We study verification problems for history-constrained systems (HCS), a model of guarded computation that uses nested systems. An outer system describes the process architecture in which a sequence of actions represents the communication…

Formal Languages and Automata Theory · Computer Science 2026-02-23 Louwe B. Kuijer , David Purser , Henry Sinclair-Banks , Patrick Totzke

Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…

Systems and Control · Electrical Eng. & Systems 2023-09-29 Laura Lützow , Matthias Althoff

A vector addition system (VAS) with an initial and a final marking and transition labels induces a language. In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision…

Formal Languages and Automata Theory · Computer Science 2018-02-20 Wojciech Czerwiński , Piotr Hofman , Georg Zetzsche

We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence,…

Logic in Computer Science · Computer Science 2015-07-01 Karsten Wolf , Harro Wimmel

Although decidable, the marking reachability problem for Petri nets is well-known to be intractable in general, and a non-elementary lower bound has been recently uncovered. In order to alleviate this difficulty, various structural and…

Logic in Computer Science · Computer Science 2020-06-11 Thomas Hujsa , Bernard Berthomieu , Silvano Dal Zilio , Didier Le Botlan

A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) \cap Lin(v) \neq \emptyset. Despite their simplicity and elegance, reachability oracles have failed to…

Databases · Computer Science 2013-07-02 Ruoming Jin , Guan Wang

Autonomous systems are increasingly implemented using end-to-end learning-based controllers. Such controllers make decisions that are executed on the real system, with images as one of the primary sensing modalities. Deep neural networks…

Machine Learning · Computer Science 2024-05-03 Yuang Geng , Jake Brandon Baldauf , Souradeep Dutta , Chao Huang , Ivan Ruchkin

We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types,…

Data Structures and Algorithms · Computer Science 2015-05-14 Boaz Patt-Shamir , Dror Rawitz

We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly…

Logic in Computer Science · Computer Science 2025-08-15 Toghrul Karimov , Edon Kelmendi , Joël Ouaknine , James Worrell

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

For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all…

Data Structures and Algorithms · Computer Science 2010-12-23 Loukas Georgiadis , Stavros D. Nikolopoulos , Leonidas Palios

We study the NP-hard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices $s$ and $t$, the goal is to delete as…

Computational Complexity · Computer Science 2018-04-25 Cristina Bazgan , Till Fluschnik , André Nichterlein , Rolf Niedermeier , Maximilian Stahlberg

We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…

Optimization and Control · Mathematics 2020-11-19 Nathanaël Fijalkow , Joël Ouaknine , Amaury Pouly , João Sousa-Pinto , James Worrell

A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. We introduce and study…

Optimization and Control · Mathematics 2016-10-19 Fabio Somenzi , Behrouz Touri , Ashutosh Trivedi

A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. Alur, Wojtczak, and…

Logic in Computer Science · Computer Science 2017-07-14 Shankara Narayanan Krishna , Aviral Kumar , Fabio Somenzi , Behrouz Touri , Ashutosh Trivedi

In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…

Systems and Control · Electrical Eng. & Systems 2021-09-17 Bineet Ghosh , Parasara Sridhar Duggirala