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Related papers: Reachability in symmetric VASS

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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

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 this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend on one another. This new model…

Computational Complexity · Computer Science 2017-01-12 Ventsislav Chonev

This note is a product of digestion of the famous proof of decidability of the reachability problem for vector addition systems with states (VASS), as first established by Mayr in 1981 and then simplified by Kosaraju in 1982. The note is…

Logic in Computer Science · Computer Science 2020-05-28 Sławomir Lasota

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 analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et…

Computational Complexity · Computer Science 2020-07-03 Stefan Jaax , Stefan Kiefer

Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the…

Computational Complexity · Computer Science 2015-07-01 Matthew Hague , C. -H. Luke Ong

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

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

Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two…

Numerical Analysis · Computer Science 2015-10-15 Oleksiy Kurganskyy , Igor Potapov

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

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 reachability problem for one-counter automata in which transitions can carry disequality tests. A disequality test is a guard that prohibits a specified counter value. This reachability problem has been known to be NP-hard and…

Formal Languages and Automata Theory · Computer Science 2024-08-23 Dmitry Chistikov , Jérôme Leroux , Henry Sinclair-Banks , Nicolas Waldburger

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

Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…

Optimization and Control · Mathematics 2014-04-24 Kendra Lesser , Meeko Oishi

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

Consider an agent traversing a graph of "gadgets", each with local state that changes with each traversal by the agent. We characterize the complexity of universal traversal, where the goal is to traverse every gadget at least once, for DAG…

Computational Complexity · Computer Science 2023-11-16 Hayashi Ani , Erik Demaine , Jenny Diomidova , Dylan Hendrickson , Jayson Lynch

This paper investigates the symmetry properties of basins of attraction and their boundaries in equivariant dynamical systems. While the symmetry groups of compact attractors are well understood, the corresponding analysis for non-compact…

Chaotic Dynamics · Physics 2025-09-16 Xiao Xie

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

By adapting the iterative yardstick construction of Stockmeyer, we show that the reachability problem for vector addition systems with a stack does not have elementary complexity. As a corollary, the same lower bound holds for the…

Formal Languages and Automata Theory · Computer Science 2013-10-08 Ranko Lazic