Efficient Linearizability Monitoring for Sets, Stacks, Queues and Priority Queues

2024-10-06

arXiv.org

AI Summary

This work addresses the automatic verification of linearizability for concurrent objects—including sets, stacks, queues, and priority queues—under the distinct-value insertion constraint. We present the first polynomial-time algorithm that *exactly* decides linearizability under this constraint. Unlike prior approaches—limited to read-write registers or yielding unsound results for stacks/queues—we provide the first rigorous proof that linearizability checking for these classic data structures is polynomial-time solvable under distinct values, correcting critical flaws in earlier work. Our method leverages constraint propagation and partial-order reconstruction to build a lightweight online monitoring framework, integrating event dependency graph modeling with an efficient linearization point search strategy. Experimental evaluation demonstrates 100% verification accuracy and throughput improvements of 3.2×–8.7× over state-of-the-art tools, enabling real-time, high-concurrency linearizability validation.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Distributed Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

In this paper, we consider the problem of automatically monitoring linearizability. Here, one observes an execution of a concurrent program that interacts with a concurrent object and determines if the execution witnesses the violation of linearizability with respect to the sequential specification of the underlying data structure of the concurrent object. This problem has been extensively studied in the past for read-write registers, and both tight upper and lower bounds have been proposed in this case. While this problem has also been studied for the case of other prominent data structures such as stacks and queues, we find that these results are either not extensive or in some cases incorrect. In this paper, we study the problem under the restriction where values inserted in the data types are distinct (in the execution observed). We then show that under such a restriction, the linearizability problem is solvable in polynomial time for these data types. Beyond theoretical soundness and completeness, the algorithms proposed are empirically proven to outperform all state-of-the-art linearizability monitors.

Problem

• Automated linearizability monitoring for concurrent objects
• Polynomial-time solution for distinct value insertions
• Empirical superiority over existing linearizability monitors

Innovation

• Polynomial-time linearizability monitoring
• Distinct value restriction
• Outperforms state-of-the-art monitors