Deductive Controller Synthesis for Probabilistic Hyperproperties
This addresses security, privacy, and system-level requirements in probabilistic systems, representing an incremental advance in controller synthesis methods.
The paper tackles the controller synthesis problem for Markov decision processes with probabilistic hyperproperties, proposing a new approach that enhances HyperPCTL with structural constraints and uses abstraction refinement to prune the search space. The result shows it considerably outperforms the state-of-the-art tool HyperProb and is the first to effectively combine probabilistic hyperproperties with additional constraints.
Probabilistic hyperproperties specify quantitative relations between the probabilities of reaching different target sets of states from different initial sets of states. This class of behavioral properties is suitable for capturing important security, privacy, and system-level requirements. We propose a new approach to solve the controller synthesis problem for Markov decision processes (MDPs) and probabilistic hyperproperties. Our specification language builds on top of the logic HyperPCTL and enhances it with structural constraints over the synthesized controllers. Our approach starts from a family of controllers represented symbolically and defined over the same copy of an MDP. We then introduce an abstraction refinement strategy that can relate multiple computation trees and that we employ to prune the search space deductively. The experimental evaluation demonstrates that the proposed approach considerably outperforms HyperProb, a state-of-the-art SMT-based model checking tool for HyperPCTL. Moreover, our approach is the first one that is able to effectively combine probabilistic hyperproperties with additional intra-controller constraints (e.g. partial observability) as well as inter-controller constraints (e.g. agreements on a common action).