Related papers: Reachability is Tower Complete
In this paper, we mainly focus on the existence and uniqueness of the vertical tensor complementarity problem. Firstly, combining the generalized-order linear complementarity problem with the tensor complementarity problem, the vertical…
The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports important results regarding the properties of the accessibility,…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
The high complexity of DNS poses unique challenges for ensuring its security and reliability. Despite continuous advances in DNS testing, monitoring, and verification, protocol-level defects still give rise to numerous bugs and attacks. In…
The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is efficient and deserves that care. It states that a vector lattice…
Exploiting tools from algebraic geometry, the problem of finiteness of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The…
This paper considers the problem of reachability analysis of control systems with optimal controllers, as a first step towards verifying the safety and correctness of such systems. Despite their appeal in guaranteeing task satisfaction…
Virtual Reality (VR) has become more and more popular with dropping prices for systems and a growing number of users. However, the issue of accessibility in VR has been hardly addressed so far and no uniform approach or standard exists at…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
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…
Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…
This paper considers the realizability of quantum gates from the perspective of information complexity. Since the gate is a physical device that must be controlled classically, it is subject to random error. We define the complexity of gate…
We consider a graph with colored edges. A trail (vertices may repeat but not edges) is called \emph{alternating} when successive edges have different colors. Given a set of vertices called \emph{terminals}, the \emph{alternating…
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…
A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be…
We show that the regular separability problem of VASS reachability languages is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that…