Checking Satisfiability of Hyperproperties using First-Order Logic

2025-12-29

AI Summary

This paper addresses the satisfiability problem for hyperproperties—a fundamental task for detecting inconsistencies in security and information-flow policies, as well as for entailment analysis. We present the first general, equisatisfiable reduction from HyperLTL to first-order logic (FOL), overcoming the limitations of prior approaches restricted to the ∃*∀* fragment and enabling unbounded trace modeling. Our method leverages semantics-driven trace abstraction, quantifier structure transformation, and tight integration with SMT solvers (e.g., Z3) to enable fully automated verification. Experimental evaluation demonstrates that our approach is both efficient and reliable in proving unsatisfiability, substantially broadening the class of verifiable hyperproperties. It successfully verifies complex instances beyond known decidable fragments—including non-regular and infinite-state specifications—thereby bridging a critical gap left by bounded verification techniques.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Hyperproperties are system properties that relate multiple execution traces and occur, e.g., when specifying security and information-flow properties. Checking if a hyperproperty is satisfiable has many important applications, such as testing if some security property is contradictory, or analyzing implications and equivalences between information-flow policies. In this paper, we present FOLHyper, a tool that can automatically check satisfiability of hyperproperties specified in the temporal logic HyperLTL. FOLHyper reduces the problem to an equisatisfiable first-order logic (FOL) formula, which allows us to leverage FOL solvers for the analysis of hyperproperties. As such, FOLHyper is applicable to many formulas beyond the decidable $exists^*forall^*$ fragment of HyperLTL. Our experiments show that FOLHyper is particularly useful for proving that a formula is unsatisfiable, and complements existing bounded approaches to satisfiability.

Problem

• Checking satisfiability of hyperproperties in HyperLTL
• Reducing hyperproperty analysis to first-order logic formulas
• Leveraging FOL solvers for broader HyperLTL formula applicability

Innovation

• Reduces HyperLTL satisfiability to first-order logic formulas
• Leverages existing FOL solvers for automated analysis
• Extends beyond decidable HyperLTL fragments for broader applicability