Parsimonious, Simulation Based Verification of Linear Systems

We present a technique to verify safety properties of linear systems (possibly time varying) using very few simulations. For a linear system of dimension n, our technique needs n+ 1 simulation runs. This is in contrast to current simulation based approaches, where the number of simulations either depends upon the number of vertices in the convex polyhedral initial set, or on the proximity of the unsafe set to the set of reachable states. At its core, our algorithm exploits the superposition principle of linear systems. Our algorithm computes both an over and an under approximation of the set of reachable states.