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Hyperproperties are system properties that require quantification overmultiple execution traces of a system. Hyperproperties can express severalspecifications of interest for cyber-physical systems--such as opacity,robustness, and noninterference--which cannot be expressed using linear-timeproperties. This paper presents for the first time a discretization-freeapproach for the formal verification of discrete-time uncertain dynamicalsystems against hyperproperties. The proposed approach involves decompositionof complex hyperproperties into several verification conditions by exploitingthe automata-based structures corresponding to the complements of the originalspecifications. These verification conditions are then discharged bysynthesizing so-called augmented barrier certificates, which provide certainsafety guarantees for the underlying system. For systems with polynomial-typedynamics, we present a sound procedure to synthesize polynomial-type augmentedbarrier certificates by reducing the problem to sum-of-squares optimizations.We demonstrate the effectiveness of our proposed approaches on two physicalcase studies against two important hyperproperties: initial-state opacity andinitial-state robustness.

Verification of Hyperproperties for Uncertain Dynamical Systems via Barrier Certificates