# Probabilistic Hyperproperties with Nondeterminism

arXiv: https://arxiv.org/abs/2005.06115 · HTML: https://mlsanity.com/paper/2005.06115/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2020.

## Built on by (most cited first, 2 of 2)

- [Causal Temporal Reasoning for Markov Decision Processes](https://mlsanity.com/paper/2212.08712/) (2022)
- [Deductive Controller Synthesis for Probabilistic Hyperproperties](https://mlsanity.com/paper/2307.04503/) (2023)

## Abstract (arXiv)

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.