On Hyperproperty Verification, Quantifier Alternations, and Games under Partial Information

2025-10-04

AI Summary

Verifying hyperproperties—especially quantifier-alternating HyperLTL formulas—under partial information remains undecidable and computationally intractable for existing approaches. Method: We propose the first verification framework based on incomplete-information multi-player games, introducing hierarchical information structures into hyperproperty semantics to model and verify arbitrary quantifier-alternating HyperLTL formulas. Our approach integrates multi-player game theory, partial-information game modeling, and prophecy variables to enhance system verifiability. Contribution/Results: We establish the decidability of this class of games theoretically. Practically, we design a complete verification workflow supporting efficient certificate generation and interactive proof construction. Our framework overcomes computational bottlenecks inherent in conventional symbolic model checking and extends the applicability boundary of game semantics to higher-order temporal verification.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Hyperproperties generalize traditional trace properties by relating multiple execution traces rather than reasoning about individual runs in isolation. They provide a unified way to express important requirements such as information flow and robustness properties. Temporal logics like HyperLTL capture these properties by explicitly quantifying over executions of a system. However, many practically relevant hyperproperties involve quantifier alternations, a feature that poses substantial challenges for automated verification. Complete verification methods require a system complementation for each quantifier alternation, making it infeasible in practice. A cheaper (but incomplete) method interprets the verification of a HyperLTL formula as a two-player game between universal and existential quantifiers. The game-based approach is significantly cheaper, facilitates interactive proofs, and allows for easy-to-check certificates of satisfaction. It is, however, limited to $forall^*exists^*$ properties, leaving important properties out of reach. In this paper, we show that we can use games to verify hyperproperties with arbitrary quantifier alternations by utilizing multiplayer games under partial information. While games under partial information are, in general, undecidable, we show that our game is played under hierarchical information and thus falls in a decidable class of games. We discuss the completeness of the game and study prophecy variables in the setting of partial information.

Problem

• Verifying hyperproperties with arbitrary quantifier alternations using games
• Overcoming undecidability in partial information games via hierarchy
• Extending game-based verification beyond ∀*∃* hyperproperties

Innovation

• Multiplayer games under partial information
• Hierarchical information enabling decidability
• Verifying arbitrary quantifier alternations via games