Verification of Hyperproperties for Dynamical Systems via Barrier Certificates

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.