We study the problem of formalizing and checking probabilistic hyperproperties for models that allow nondeterminism in actions. We extend the temporal logic \HyperPCTL, which has been previously introduced for discrete-time Markov chains, to enable the specification of hyperproperties also for Markov decision processes. We generalize HyperPCTL by allowing explicit and simultaneous quantification over schedulers and probabilistic computation trees and show that it can express important quantitative requirements in security and privacy. We show that HyperPCTL model checking over MDPs is in general undecidable for quantification over probabilistic schedulers with memory, but restricting the domain to memoryless non-probabilistic schedulers turns the model checking problem decidable. Subsequently, we propose an SMT-based encoding for model checking this language and evaluate its performance.

中文翻译：

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具有不确定性的概率超性质

我们研究了在动作中允许不确定性的模型的形式化和检查概率超属性的问题。我们扩展了之前为离散时间马尔可夫链引入的时间逻辑 \HyperPCTL，以支持马尔可夫决策过程的超属性规范。我们通过允许对调度程序和概率计算树进行显式和同时量化来概括 HyperPCTL，并表明它可以表达安全和隐私方面的重要量化要求。我们表明，对 MDP 的 HyperPCTL 模型检查对于具有内存的概率调度器的量化通常是不可判定的，但是将域限制为无记忆的非概率调度器会使模型检查问题变得可判定。随后，