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In this paper, we propose a scalable and highly efficient index structure for the reachability problem over graphs. We build on the well-known node interval labeling scheme where the set of vertices reachable from a particular node is…
Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
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…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
Reachability analysis plays a central role in low-thrust spacecraft trajectory optimization by identifying which target states can be achieved under constraints on time, thrust, and propellant. Classical approaches construct reachable sets…
We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter…
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 $R$,…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
In the real world a graph is often fragmented and distributed across different sites. This highlights the need for evaluating queries on distributed graphs. This paper proposes distributed evaluation algorithms for three classes of queries:…
Vector joins - finding all vector pairs between a set of query and data vectors whose distances are below a given threshold - are fundamental to modern vector and vector-relational database systems that power multimodal retrieval and…
The reachability problem asks to decide if there exists a path from one vertex to another in a digraph. In a grid digraph, the vertices are the points of a two-dimensional square grid, and an edge can occur between a vertex and its…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
Approximate Nearest Neighbor Search (ANNS) is essential for various data-intensive applications, including recommendation systems, image retrieval, and machine learning. Scaling ANNS to handle billions of high-dimensional vectors on a…
The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known…
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…
Reachability analysis is a popular method to give safety guarantees for stochastic cyber-physical systems (SCPSs) that takes in a symbolic description of the system dynamics and uses set-propagation methods to compute an overapproximation…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…