What Cannot Be Implemented on Weak Memory?

TL;DR

This paper introduces a methodology to prove the impossibility of implementing certain concurrent objects on weak memory models by analyzing their mergeability properties, leading to new bounds and separation results.

Contribution

It provides a general approach to establish impossibility results for object implementations on various weak memory models using mergeability characterizations.

Findings

Impossible to implement standard distributed objects on certain weak memory models.

Identified tight bounds for object implementability under different memory restrictions.

Established new separation results between weak memory models and object classes.

Abstract

We present a general methodology for establishing the impossibility of implementing certain concurrent objects on different (weak) memory models. The key idea behind our approach lies in characterizing memory models by their mergeability properties, identifying restrictions under which independent memory traces can be merged into a single valid memory trace. In turn, we show that the mergeability properties of the underlying memory model entail similar mergeability requirements on the specifications of objects that can be implemented on that memory model. We demonstrate the applicability of our approach to establish the impossibility of implementing standard distributed objects with different restrictions on memory traces on three memory models: strictly consistent memory, total store order, and release-acquire. These impossibility results allow us to identify tight and almost tight bounds for some objects, as well as new separation results between weak memory models, and between well-studied objects based on their implementability on weak memory models.