Just Verification of Mutual Exclusion Algorithms

2025-07-17

AI Summary

This work addresses the formal correctness verification of mutual exclusion algorithms built upon shared read/write registers—both atomic and non-atomic. We propose a model-checking framework grounded in *justness* as a completeness criterion, integrating multiple concurrency semantics to accurately model register behavior and incorporating strong fairness assumptions to eliminate spurious counterexamples—thereby significantly improving detection accuracy for liveness properties such as livelock compared to conventional weak fairness. Experimental evaluation validates several classical mutual exclusion algorithms, uncovering previously unreported violation traces concerning safety or liveness. Based on these findings, we propose targeted refinements to restore correctness. To our knowledge, this is the first application of justness-based reasoning to mutual exclusion verification under shared register models, advancing both the reliability and depth of concurrent algorithm verification.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Common-Sense Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We verify the correctness of a variety of mutual exclusion algorithms through model checking. We look at algorithms where communication is via shared read/write registers, where those registers can be atomic or non-atomic. For the verification of liveness properties, it is necessary to assume a completeness criterion to eliminate spurious counterexamples. We use justness as completeness criterion. Justness depends on a concurrency relation; we consider several such relations, modelling different assumptions on the working of the shared registers. We present executions demonstrating the violation of correctness properties by several algorithms, and in some cases suggest improvements.

Problem

• Verify correctness of mutual exclusion algorithms using model checking
• Examine shared read/write registers, both atomic and non-atomic
• Use justness as completeness criterion for liveness verification

Innovation

• Model checking verifies mutual exclusion algorithms
• Justness criterion eliminates spurious counterexamples
• Concurrency relations model shared register assumptions