The Power of Strong Linearizability: the Difficulty of Consistent Refereeing

TL;DR

This paper explores the complexity of achieving consistent refereeing in concurrent systems with strong linearizability, revealing that such implementations require high coordination power and are limited by fundamental impossibility results.

Contribution

It introduces contest objects that capture the power of strong linearizability, demonstrating their limitations and the high coordination needed for consistent refereeing in concurrent objects.

Findings

Strong linearizability entails a form of agreement weaker than consensus.

Impossibility results for strong linearizability extend to high-level objects like queues and counters.

Achieving consistent refereeing requires high coordination power, as shown by the introduced contest objects.

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 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.