Tractable Hyperproperties for MDPs

2026-04-08

AI Summary

Existing probabilistic hyperlogics such as HyperPCTL and PHL suffer from undecidable model checking over Markov decision processes (MDPs), hindering efficient verification of probabilistic safety and privacy properties across multiple execution traces. This work focuses on a decidable fragment that supports equality relations between event probabilities and conjunctive combinations of reachability, safety, and Büchi objectives. By integrating formal methods, automata theory, and linear programming, the paper provides the first systematic characterization and efficient solution procedure for this subclass, thereby circumventing the undecidability barrier inherent in general hyperlogics. The proposed algorithms achieve tight complexity bounds for certain problem instances, and the accompanying tool demonstrates speedups of several orders of magnitude over general-purpose solvers on benchmark cases.

Abstract

Probabilistic hyperproperties describe probabilistic relations between multiple sets of executions in a stochastic system. Prominent examples include information-theoretic characterizations of security and privacy policies. However, model checking for existing probabilistic hyperlogics, such as HyperPCTL and PHL, is undecidable in Markov decision processes (MDPs). In this paper, we study an underexplored problem: the verification of fragments of probabilistic hyperproperties that relate the probabilities of different events to each other, possibly across independent executions of an MDP. Representative verification questions include: Can two different target states be reached from the same initial state with the same probability? (different events), Can a given target state be reached from two different initial states with the same probability? (same event, independent executions), and natural combinations of these forms. Besides reachability, our relational probabilistic properties cover safety, Büchi, and coBüchi objectives. They can also be combined conjunctively, thereby generalizing standard multi-objective MDP properties. We provide efficient algorithms for relevant classes of relational properties, while proving computational hardness and completeness results for others. An implementation of our approach outperforms solvers for more general probabilistic hyperlogics by orders of magnitude on the subset of their benchmarks that lies within our fragment.

Problem

• probabilistic hyperproperties
• Markov decision processes
• model checking
• relational probabilistic properties
• undecidability

Innovation

• relational probabilistic properties
• tractable verification
• Markov decision processes
• hyperproperties
• model checking