Abstract
Hyperproperties are properties that describe the correctness of a system as a relation between multiple executions. Hyperproperties generalize trace properties and include information-flow security requirements, like noninterference, as well as requirements like symmetry, partial observation, robustness, and fault tolerance. We initiate the study of the specification and verification of hyperproperties of Markov decision processes (MDPs). We introduce the temporal logic PHL (Probabilistic Hyper Logic), which extends classic probabilistic logics with quantification over schedulers and traces. PHL can express a wide range of hyperproperties for probabilistic systems, including both classical applications, such as probabilistic noninterference, and novel applications in areas such as robotics and planning. While the model checking problem for PHL is in general undecidable, we provide methods both for proving and for refuting formulas from a fragment of the logic. The fragment includes many probabilistic hyperproperties of interest.
This work was partially supported by the Collaborative Research Center “Foundations of Perspicuous Software Systems” (TRR 248, 389792660), the European Research Council (ERC) Grant OSARES (No. 683300), the DARPA Assured Autonomy program, the iCyPhy center, and by Berkeley Deep Drive.
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Notes
- 1.
In the literature, schedulers are also known as strategies or policies.
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Dimitrova, R., Finkbeiner, B., Torfah, H. (2020). Probabilistic Hyperproperties of Markov Decision Processes. In: Hung, D.V., Sokolsky, O. (eds) Automated Technology for Verification and Analysis. ATVA 2020. Lecture Notes in Computer Science(), vol 12302. Springer, Cham. https://doi.org/10.1007/978-3-030-59152-6_27
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