Related papers: Reachability in fixed dimension vector addition sy…
Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
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…
We introduce a technique for reachability analysis of Time-Basic (TB) Petri nets, a powerful formalism for real- time systems where time constraints are expressed as intervals, representing possible transition firing times, whose bounds are…
The problem of graph Reachability is to decide whether there is a path from one vertex to another in a given graph. In this paper, we study the Reachability problem on three distinct graph families - intersection graphs of Jordan regions,…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are,…
We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds…
Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these…
In this paper, we study networks of discrete-time linear time-invariant subsystems. Our focus is on situations where subsystems are connected to each other through a time-invariant topology and where there exists a base-station whose aim is…
Coverability in Petri nets finds applications in verification of safety properties of reactive systems. We study coverability in the equivalent model: Vector Addition Systems with States (VASS). A k-VASS can be seen as k counters and a…
We propose a method for checking generalized reachability properties in Petri nets that takes advantage of structural reductions and that can be used, transparently, as a pre-processing step of existing model-checkers. Our approach is based…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
We study detectability properties for labeled Petri nets and finite automata. We first study weak approximate detectability (WAD) that implies that there exists an infinite observed output sequence of the system such that each prefix of the…
The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped…
In a previous paper we introduced immediate observation Petri nets, a subclass of Petri nets with application domains in distributed protocols (population protocols) and theoretical chemistry (chemical reaction networks). IO nets enjoy many…