Probabilistic Hyperproperties with Rewards

Oyendrila Dobe, Lukas Wilke, Erika Ábrahám, Ezio Bartocci, Borzoo Bonakdarpour

Abstract: Probabilistic hyperproperties describe system properties that are concerned with the probability relation between different system executions. Likewise, it is desirable to relate performance metrics (e.g., energy, execution time, etc.) between multiple runs. This paper introduces the notion of rewards to the temporal logic HyperPCTL by extending the syntax and semantics of the logic to express the accumulated reward relation among different computations. We demonstrate the application of the extended logic in expressing side-channel timing countermeasures, efficiency in probabilistic conformance, path planning in robotics applications, and recovery time in distributed self-stabilizing systems. We also propose a model checking algorithm for verifying Markov Decision Processes against HyperPCTL with rewards and report experimental results.