Verification of Hyperproperties for Dynamical Systems via Barrier Certificates

Mahathi Anand, Vishnu Murali, Ashutosh Trivedi, Majid Zamani

Abstract: Hyperproperties are system properties that require quantification over multiple execution traces of a system. Hyperproperties can express several specifications of interest for cyber–physical systems—such as opacity, robustness, and noninterference—which cannot be expressed using linear time properties. This article presents for the first time a discretization-free approach for the formal verification of discrete-time dynamical systems against hyperproperties. The proposed approach involves the decomposition of complex hyperproperties into several verification conditions by exploiting the automata-based structures corresponding to the complements of the original specifications. These verification conditions are then discharged by synthesizing so-called augmented barrier certificates, which provide certain safety guarantees for the underlying system. For systems with polynomial-type dynamics, we present a sound procedure to synthesize polynomial-type augmented barrier certificates by reducing the problem to sum-of-squares optimizations. We demonstrate the effectiveness of our proposed approaches on two physical case studies against two important hyperproperties: initial-state opacity and initial-state robustness.