Verifying Tolerant Systems Using Polynomial Approximations

In this paper, we approximate a hybrid system with arbitrary flow functions by systems with polynomial flows; the verification of certain properties in systems with polynomial flows can be reduced to the first order theory of reals, and is therefore decidable. The polynomial approximations that we construct ¿-simulate (as opposed to "simulate\´\´) the original system, and at the same time are tight. We show that for systems that we call tolerant, safety verification of a system can be reduced to the safety verification of the polynomial approximation. Our main technical tool in proving this result is a logical characterization of ¿-simulations. We demonstrate the construction of the polynomial approximation, as well as the verification process, by applying it to an example protocol in air traffic coordination.