Related papers: A Logical Product Approach to Zonotope Intersectio…
This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…
We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…
Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $\epsilon \in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $\epsilon_i \epsilon_j$.…
Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization…
We present a new idea to adapt relational abstract domains to the analysis of IEEE 754-compliant floating-point numbers in order to statically detect, through abstract Interpretation-based static analyses, potential floating-point run-time…
This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The major contribution of…
Polynomial zonotopes, a non-convex set representation, have a wide range of applications from real-time motion planning and control in robotics, to reachability analysis of nonlinear systems and safety shielding in reinforcement learning.…
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…
Reachability analysis for hybrid nonaffine systems remains computationally challenging, as existing set representations--including constrained, polynomial, and hybrid zonotopes--either lose tightness under high-order nonaffine maps or…
This paper lays a practical foundation for using abstract interpretation with an abstract domain that consists of sets of quantified first-order logic formulas. This abstract domain seems infeasible at first sight due to the complexity of…
This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x-y<=c) and (+/-x<=c), where x and y are variables values and c is an integer or…
We present a new abstract interpretation framework for the precise over-approximation of numerical fixpoint iterators. Our key observation is that unlike in standard abstract interpretation (AI), typically used to over-approximate all…
The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing…
In this paper, we propose reachability analysis using constrained polynomial logical zonotopes. We perform reachability analysis to compute the set of states that could be reached. To do this, we utilize a recently introduced set…
We present abstract acceleration techniques for computing loop invariants for numerical programs with linear assignments and conditionals. Whereas abstract interpretation techniques typically over-approximate the set of reachable states…
Verification and synthesis of Cyber-Physical Systems (CPS) are challenging and still raise numerous issues so far. In this paper, based on a new concept of mixed sets defined as function images of symbol type domains, a compositional…
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…
Abstract interpretation is a well-established technique for performing static analyses of logic programs. However, choosing the abstract domain, widening, fixpoint, etc. that provides the best precision-cost trade-off remains an open…
Hybrid systems play a crucial role in modeling real-world applications where discrete and continuous dynamics interact, including autonomous vehicles, power systems, and traffic networks. Safety verification for these systems requires…
Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers.…