Related papers: Reachable Set Estimation and Safety Verification f…

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…

We present a controller synthesis algorithm for reach-avoid problems for piecewise linear discrete-time systems. Our algorithm relies on SMT solvers and in this paper we focus on piecewise constant control strategies. Our algorithm…

Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address…

Relu Fully Connected Networks are ubiquitous but uninterpretable because they fit piecewise linear functions emerging from multi-layered structures and complex interactions of model weights. This paper takes a novel approach to piecewise…

Given a stable linear time-invariant (LTI) system subject to output constraints, we present a method to compute a set of disturbances such that the reachable set of outputs matches as closely as possible the output constraint set, while…

Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is either assumed to be known a priori or estimated from data…

Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural…

Ensuring safety in autonomous systems with vision-based control remains a critical challenge due to the high dimensionality of image inputs and the fact that the relationship between true system state and its visual manifestation is…

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of…

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…

It has been widely assumed that a neural network cannot be recovered from its outputs, as the network depends on its parameters in a highly nonlinear way. Here, we prove that in fact it is often possible to identify the architecture,…

Provable safety is one of the most critical challenges in automated driving. The behavior of numerous traffic participants in a scene cannot be predicted reliably due to complex interdependencies and the indiscriminate behavior of humans.…

We consider the problem of verifying safety for a pair of identical integrator agents in continuous time with compact set-valued input uncertainties. We encode this verification problem as that of certifying or falsifying the intersection…

Reachability queries checking the existence of a path from a source node to a target node are fundamental operators for querying and processing graph data. Current approaches for index-based evaluation of reachability queries either focus…

Neural networks with ReLU activation play a key role in modern machine learning. Understanding the functions represented by ReLU networks is a major topic in current research as this enables a better interpretability of learning processes.…

Designing provably safe control is a core problem in trustworthy autonomy. However, most prior work in this regard assumes either that the system dynamics are known or deterministic, or that the state and action space are finite,…

In this paper, we consider the computational complexity of formally verifying the behavior of Rectified Linear Unit (ReLU) Neural Networks (NNs), where verification entails determining whether the NN satisfies convex polytopic…

Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output. Conversely, there may exist large, meaningful perturbations that do not…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…