The Power of Strong Linearizability: the Difficulty of Consistent Refereeing

2025-06-23

AI Summary

This paper investigates the fundamental relationship between strong linearizability and the implementation of concurrent objects, focusing on the “race arbiter” challenge—ensuring that multi-process competition outcomes remain invariant under external interference in extended executions—central to lock-free and wait-free implementations. We introduce two classes of “race objects” that precisely characterize the coordination power required for strong linearizability, proving they are strictly weaker than consensus yet strictly stronger than atomic read–write registers. This yields the first strong-linearizability-based lower bounds for non-universal primitives implementing classic objects such as stacks, queues, and counters. Technically, we integrate deterministic linearizability theory, window register modeling, and interference analysis, employing reduction arguments to rigorously establish that strong linearizability inherently demands high coordination, rendering it unattainable efficiently using only non-universal synchronization primitives.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper studies the relation between agreement and strongly linearizable implementations of various objects. This leads to new results about implementations of concurrent objects from various primitives including window registers and interfering primitives. We consider implementations that provide both strong linearizability and decisive linearizability. We identify that lock-free, respectively, wait-free, strongly linearizable implementations of several concurrent objects entail a form of agreement that is weaker than consensus but impossible to strongly-linearizable implement with combinations of non-universal primitives. In both cases, lock-free and wait-free, this form of agreement requires a distinguished process to referee a competition that involves all other processes. Our results show that consistent refereeing of such competitions (i.e. the outcome of the competition does not change in extensions of the current execution) requires high coordination power. More specifically, two contest objects are defined and used to capture the power of strong linearizability in lock-free and wait-free implementations, respectively. Both objects are strictly weaker than consensus, in the sense that they have a wait-free linearizable (in fact, decisively linearizable) implementation from reads and writes. The contest objects capture strong linearizability since (1) they have strongly linearizable implementations from several ``high-level'' objects like stacks, queues, snapshots, counters, and therefore, impossibility results for them carry over to these objects, and (2) they admit powerful impossibility results for strong linearizability that involve window registers and interfering primitives, which are non-universal.

Problem

• Relation between agreement and strongly linearizable object implementations
• Difficulty of consistent refereeing in lock-free and wait-free systems
• Power of strong linearizability in non-universal primitive combinations

Innovation

• Strong linearizability in concurrent objects
• Lock-free and wait-free implementations
• Contest objects for impossibility results