Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model Reduction

Abstract

We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a nite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property, allows us to conclude whether the original stochastic hybrid system meets its temporal logic speci cations. We present the rst statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in the linear inequality linear temporal logic (iLTL) or the metric interval temporal logic (MITL).CCS Concepts: •Computer systems organization → Embedded and cyber-physical systems; •Security and privacy → Formal methods and theory of security; • eory of computation → Abstraction;