Verification Using Simulation

Verification and simulation have always been complementary, if not competing, approaches to system design. In this paper, we present a novel method for so-called metric transition systems that bridges the gap between verification and simulation, enabling system verification using a finite number of simulations. The existence of metrics on the system state and observation spaces, which is natural for continuous systems, allows us to capitalize on the recently developed framework of approximate bisimulations, and infer the behavior of neighborhood of system trajectories around a simulated trajectory. For nondeterministic linear systems that are robustly safe or robustly unsafe, we provide not only a completeness result but also an upper bound on the number of simulations required as a function of the distance between the reachable set and the unsafe set. Our framework is the first simulation-based verification method that enjoys completeness for infinite-state systems. The complexity is low for robustly safe or robustly unsafe systems, and increases for nonrobust problems. This provides strong evidence that robustness dramatically impacts the complexity of system verification and design.