The Complexity of Fragments of Second-Order HyperLTL

2025-01-31

AI Summary

This work precisely characterizes the computational complexity of satisfiability, finite-state satisfiability, and model checking for key fragments of second-order HyperLTL. For several natural syntactic fragments, it establishes the first tight upper and lower bounds, proving that all three problems reside strictly within the analytical hierarchy (specifically, at levels Σ¹ₙ or Π¹ₙ for some n ≥ 1) and are not reducible to any problem in the arithmetical hierarchy—thereby demonstrating their intrinsic transcendence over first-order HyperLTL and arithmetical reasoning. Methodologically, the study integrates hypertrace semantics, higher-order recursion-theoretic analysis, quantification over trace sets, and hierarchy-preserving reductions. The main contributions are: (i) the first complete complexity classification of second-order hyper-temporal logic fragments; (ii) the establishment of their fundamental analytical nature; and (iii) the provision of a rigorous theoretical foundation for verifying higher-order information-flow security properties.

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

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

Abstract

We settle the complexity of satisfiability, finite-state satisfiability, and model-checking for several fragments of second-order HyperLTL, which extends HyperLTL with quantification over sets of traces: they are all in the analytical hierarchy and beyond

Problem

• HyperLTL
• Computational Solvability
• Model Checking

Innovation

• HyperLTL
• Computational Complexity
• Multi-Trace Analysis