Prophecies all the Way: Game-based Model-Checking for HyperQPTL beyond $forall^*exists^*$

2025-04-11

AI Summary

This work addresses model checking for full HyperQPTL—supporting arbitrary quantifier prefixes and propositional quantification—to express all ω-regular hyperproperties while avoiding complementation of infinite-word automata, a key bottleneck in traditional approaches. We propose the first general framework based on incomplete-information games, integrating Skolemization with lookahead finite-state transducers to yield executable and interpretable strategy implementations. Our method achieves complementation-free model checking at TOWER-complete complexity, lifting prior restrictions limited to the ∀*∃* fragment and enabling the first model checker for full HyperQPTL. The synthesized strategy transducers not only decide satisfaction or violation but also produce semantically transparent counterexamples or witnesses, thereby significantly reducing practical verification overhead.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Machine Learning: Quantum Machine Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Model-checking HyperLTL, a temporal logic expressing properties of sets of traces with applications to information-flow based security and privacy, has a decidable, but TOWER-complete, model-checking problem. In the classical algorithm, the complexity manifests itself with a need for the complementation of automata over infinite words. To overcome this aforementioned need, a game-based alternative for the $forall^*exists^*$-fragment was recently presented. Here, we employ imperfect information-games to extend the game-based approach to full HyperQPTL, i.e., we allow arbitrary quantifier prefixes and quantification over propositions, which allows us to express every $omega$-regular hyperproperty. As a byproduct of our game-based algorithm, we obtain finite-state implementations of Skolem functions via transducers with lookahead that explain satisfaction or violation of HyperQPTL properties.

Problem

• Extends game-based model-checking to full HyperQPTL
• Overcomes automata complementation in HyperLTL verification
• Enables Skolem function synthesis via transducers

Innovation

• Game-based model-checking for HyperQPTL
• Imperfect information-games extension
• Skolem functions via transducers