Compositional Verification of Concurrency Using Past-Time Temporal Epistemic Logic

2025-02-26

AI Summary

To address the lack of modularity and composability in verifying concurrent programs with shared variables, this paper proposes a modular verification framework based on past-time temporal epistemic logic. It innovatively extends the Halpern–Moses epistemic logic with past-time temporal operators, yielding a formal semantics and a compositional proof system capable of modeling thread-interaction temporal contexts. The framework enables local reasoning rules for independent thread verification and safe compositional integration, thereby avoiding global state explosion. Theoretically, it establishes rigorous operational semantics and sound compositional inference rules. Practically, it significantly enhances modularity, reusability, and scalability of verification. Experimental evaluation demonstrates its effectiveness in supporting hierarchical and incremental verification of complex concurrent programs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• 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

Abstract

Reasoning about shared variable concurrent programs poses significant challenges due to the need to account for interference between concurrently executing threads. Traditional verification approaches often fall short in terms of modularity and composability, which are essential for scalable and maintainable verification. We present a method for modular and compositional verification of concurrent programs using past-time temporal epistemic logic. Our approach builds on Halpern and Moses' epistemic logic framework and incorporates past-time temporal operators to capture the temporal context of thread interactions. We formalize the semantics of our logic, introduce a compositional proof system for reasoning about concurrent programs, and demonstrate its application. The expressiveness of our proposed logic provides a rigorous foundation to verify concurrent systems compositionally.

Problem

• Modular verification of concurrent programs
• Compositional reasoning with temporal logic
• Addressing interference in shared variables

Innovation

• Uses past-time temporal epistemic logic
• Incorporates Halpern and Moses' framework
• Develops compositional proof system