A Forward Simulation-Based Hierarchy of Linearizable Concurrent Objects

2026-01-15

AI Summary

This work addresses the systematic characterization and verification of linearizable concurrent objects. The authors introduce a hierarchy of linearizable objects satisfying varying liveness conditions—such as wait-freedom and lock-freedom—based on forward simulation, and prove that this hierarchy forms a bounded lattice or semilattice under forward simulation. A key contribution is a novel forward simulation criterion equivalent to linearizability, which enables compositional reasoning. The study further reveals mutual simulation relationships among strongly linearizable objects and demonstrates the framework’s effectiveness for automated verification through concrete examples—such as simulating a Herlihy–Wing queue with a timestamped queue—and a universal specification object 𝒰_Spec.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

In this paper, we systematically investigate the connection between linearizable objects and forward simulation. We prove that the sets of linearizable objects satisfying wait-freedom (resp., lock-freedom or obstruction-freedom) form a bounded join-semilattice under the forward simulation relation, and that the sets of linearizable objects without liveness constraints form a bounded lattice under the same relation. As part of our lattice result, we propose an equivalent characterization of linearizability by reducing checking linearizability w.r.t. sequential specification $Spec$ into checking forward simulation by an object $\mathcal{U}_{Spec}$. To demonstrate the forward simulation relation between linearizable objects, we prove that the objects that are strongly linearizable w.r.t. the same sequential specification and are wait-free (resp., lock-free, obstruction-free) simulate each other, and we prove that the time-stamped queue simulates the Herlihy-Wing queue. We also prove that the Herlihy-Wing queue is simulated by $\mathcal{U}_{Spec}$, and thus, our equivalent characterization of linearizability can be used in the verification of linearizability.

Problem

• linearizability
• forward simulation
• concurrent objects
• wait-freedom
• liveness

Innovation

• linearizability
• forward simulation
• concurrent objects
• liveness properties
• verification