What Cannot Be Implemented on Weak Memory?

TL;DR

The paper addresses which concurrent objects cannot be implemented on weak memory models. It introduces mergeability of traces and the Merge Theorem, connecting memory-level mergeability to object-level histories. Applying this framework to $SCM$, $TSO$, and $RA$, it derives general impossibility results and identifies fence/RMW-based constructions that are optimal or tight, including separations such as between max-register, snapshot, and counter under $RA$. This methodology guides both theoretical understanding and practical design of concurrent data structures on modern hardware.

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.