Statistical Model Checking for Probabilistic Hyperproperties
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In this paper, we propose the temporal logic HyperPCTL^* that extends PCTL^* and HyperPCTL to reason about probabilistic hyperproperties. It allows expressing probabilistic hyperproperties with nested temporal and probability operators. We show that HyperPCTL can express important probabilistic information-flow security policies. Furthermore, for the first time, we investigate statistical model checking (SMC) algorithms for HyperPCTL^* specifications in discrete-time Markov chains (DTMC). To this end, we first study SMC for HyperPCTL^* specifications with non-nested probability operators for a desired confidence or significance level. Unlike existing SMC algorithms which are based on sequential probability ratio tests (SPRT), we use the Clopper-Pearson confidence interval to avoid the need of a priori knowledge on the indifference margin. Then, we extend the proposed SMC algorithms to HyperPCTL^* specifications with multiple probability operators that are nested in different ways. Finally, we evaluate the proposed algorithms on two examples, dining cryptographers and probabilistic causation.
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