Bounded Verification with On-the-Fly Discrepancy Computation

TL;DR

This paper introduces a novel algorithm for computing discrepancy functions in simulation-based verification, removing the need for user-provided annotations and enhancing efficiency and scalability for nonlinear and hybrid systems.

Contribution

It presents a method to compute piece-wise exponential discrepancy functions automatically, improving verification accuracy and efficiency without requiring prior model annotations.

Findings

Effective in benchmark problems

Scales reasonably to larger systems

Outperforms some existing tools

Abstract

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing reachtubes from simulations. In this paper, we eliminate this requirement by presenting an algorithm for computing piece-wise exponential discrepancy functions. The algorithm relies on computing local convergence or divergence rates of trajectories along a simulation using a coarse over-approximation of the reach set and bounding the maximal eigenvalue of the Jacobian over this over-approximation. The resulting discrepancy function preserves the soundness and the relative completeness of the verification algorithm. We also provide a coordinate transformation method to improve the local estimates for the convergence or divergence rates in practical examples. We extend the method to get the input-to-state discrepancy of nonlinear dynamical systems which can be used for compositional analysis. Our experiments show that the approach is effective in terms of running time for several benchmark problems, scales reasonably to larger dimensional systems, and compares favorably with respect to available tools for nonlinear models.