Just Verification of Mutual Exclusion Algorithms with (Non-)Blocking and (Non-)Atomic Registers

2026-04-01

AI Summary

This work addresses the problem of spurious counterexamples arising from model incompleteness in the liveness verification of mutual exclusion algorithms based on (non-)blocking and (non-)atomic shared registers. To resolve this issue, we introduce justness as a completeness criterion and integrate it with concurrency relations induced by different register semantics to construct a precise model-checking framework. This approach successfully uncovers correctness flaws in several classic mutual exclusion algorithms under specific register assumptions and enables the development of effective corrections. By aligning the verification model more faithfully with the underlying concurrency semantics, our method significantly enhances both the reliability and practical applicability of algorithmic verification for mutual exclusion protocols.

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

• mutual exclusion
• model checking
• justness
• atomic registers
• liveness

Innovation

• justness
• model checking
• mutual exclusion
• non-atomic registers
• liveness verification