Verifying Asynchronous Hyperproperties in Reactive Systems

2025-12-29

AI Summary

This work addresses the model checking problem for asynchronous hyperproperties—such as observational determinism and noninterference—in reactive systems. Existing synchronous logics (e.g., HyperLTL) cannot express trajectory comparisons with asynchronous alignments across time steps, while prior asynchronous extensions (e.g., A-HLTL) support verification only for terminating systems or syntactically restricted fragments. To overcome these limitations, we propose the first game-based verification framework for arbitrary ∀*∃*-alternating asynchronous HyperLTL formulas. Our approach models stuttering-aligned trajectory generation as a two-player game, integrating automata-theoretic constructions with symbolic model checking to achieve sound, complete, and decidable verification. This is the first method enabling finite-state decision procedures for general asynchronous hyperproperties in reactive systems, significantly broadening the class of security-relevant hyperproperties amenable to automated verification.

Technology Category

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

Application Category

• 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
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Hyperproperties are system properties that relate multiple execution traces and commonly occur when specifying information-flow and security policies. Logics like HyperLTL utilize explicit quantification over execution traces to express temporal hyperproperties in reactive systems, i.e., hyperproperties that reason about the temporal behavior along infinite executions. An often unwanted side-effect of such logics is that they compare the quantified traces synchronously. This prohibits the logics from expressing properties that compare multiple traces asynchronously, such as Zdancewic and Myers's observational determinism, McLean's non-inference, or stuttering refinement. We study the model-checking problem for a variant of asynchronous HyperLTL (A-HLTL), a temporal logic that can express hyperproperties where multiple traces are compared across timesteps. In addition to quantifying over system traces, A-HLTL features secondary quantification over stutterings of these traces. Consequently, A-HLTL allows for a succinct specification of many widely used asynchronous hyperproperties. Model-checking A-HLTL requires finding suitable stutterings, which, thus far, has been only possible for very restricted fragments or terminating systems. In this paper, we propose a novel game-based approach for the verification of arbitrary $forall^*exists^*$ A-HLTL formulas in reactive systems. In our method, we consider the verification as a game played between a verifier and a refuter, who challenge each other by controlling parts of the underlying traces and stutterings. A winning strategy for the verifier then corresponds to concrete witnesses for existentially quantified traces and asynchronous alignments for existentially quantified stutterings. We identify fragments for which our game-based interpretation is complete and thus constitutes a finite-state decision procedure.

Problem

• Model-checking asynchronous hyperproperties in reactive systems
• Overcoming synchronous trace comparison limitations in logics
• Verifying arbitrary ∀*∃* A-HLTL formulas via game-based approach

Innovation

• Asynchronous HyperLTL quantifies over trace stutterings
• Game-based verification interprets model-checking as adversarial play
• Finite-state decision procedure for specific formula fragments