A Complexity-Based Hierarchy for Multiprocessor Synchronization

TL;DR

This paper introduces a new hierarchy based on space complexity to classify multiprocessor synchronization instructions, addressing limitations of the traditional computability-based hierarchy when applied to real-world memory operations.

Contribution

It proposes a novel complexity-based hierarchy for synchronization instructions, providing a more practical classification aligned with real-world usage and analyzing the power of buffered and multi-location instructions.

Findings

Hierarchy classifies instructions by space complexity in solving consensus

Buffered read/write instructions are characterized by tight bounds

Multi-location atomic assignments are similarly analyzed

Abstract

For many years, Herlihy's elegant computability based Consensus Hierarchy has been our best explanation of the relative power of various types of multiprocessor synchronization objects when used in deterministic algorithms. However, key to this hierarchy is treating synchronization instructions as distinct objects, an approach that is far from the real-world, where multiprocessor programs apply synchronization instructions to collections of arbitrary memory locations. We were surprised to realize that, when considering instructions applied to memory locations, the computability based hierarchy collapses. This leaves open the question of how to better capture the power of various synchronization instructions. In this paper, we provide an approach to answering this question. We present a hierarchy of synchronization instructions, classified by their space complexity in solving obstruction-free consensus. Our hierarchy provides a classification of combinations of known instructions that seems to fit with our intuition of how useful some are in practice, while questioning the effectiveness of others. We prove an essentially tight characterization of the power of buffered read and write instructions.Interestingly, we show a similar result for multi-location atomic assignments.