Synchronous Team Semantics for Temporal Logics

2024-09-27

arXiv.org

AI Summary

Linear Temporal Logic (LTL) and Computation Tree Logic (CTL) lack direct expressiveness for hyperproperties—properties relating multiple computation traces—limiting their applicability to information-flow security and other hyperproperty verification tasks. Method: We introduce *synchronous team semantics*, the first unified semantic framework for LTL and CTL that natively supports hyperproperty reasoning. This semantics enables natural specification of trace-relational properties (e.g., noninterference) and overcomes HyperLTL’s restriction to prefix-aligned quantification, while improving both expressive flexibility and algorithmic efficiency. Results: We precisely characterize the computational complexity of key reasoning tasks: under LTL team semantics, satisfiability is PSPACE-complete and model checking EXPTIME-complete; under CTL team semantics, the complexities are reversed—EXPTIME-complete for satisfiability and PSPACE-complete for model checking. Our work establishes a novel paradigm for equipping temporal logics with rigorous, efficient hyperproperty verification capabilities.

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

• 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 heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Data transparency and provenance

Abstract

We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have in the last decade been identified as a key concept in the verification of information flow properties. We study basic properties of the logic and classify the computational complexity of its satisfiability, path, and model checking problem. Further, we examine how extensions of the basic logic react to adding additional atomic operators. Finally, we compare its expressivity to the one of HyperLTL, another recently introduced logic for hyperproperties. Our results show that LTL with team semantics is a viable alternative to HyperLTL, which complements the expressivity of HyperLTL and has partially better algorithmic properties. For CTL with team semantics, we investigate the computational complexity of the satisfiability and model checking problem. The satisfiability problem is shown to be EXPTIME-complete while we show that model checking is PSPACE-complete.

Problem

• Extends LTL and CTL with team semantics for hyperproperty verification
• Analyzes computational complexity of satisfiability and model checking problems
• Compares expressivity with HyperLTL as alternative specification logic

Innovation

• Team semantics extends LTL for hyperproperty verification
• Team semantics adapts CTL for branching-time specifications
• LTL with team semantics complements HyperLTL expressivity