Strong Linearizability using Primitives with Consensus Number 2

TL;DR

This paper explores the possibility of implementing strongly-linearizable concurrent objects with primitives that have low consensus numbers, showing positive results for some objects and limitations for others.

Contribution

It demonstrates that many objects with consensus number 1 can be implemented strongly-linearly, and some with consensus number 2 can be implemented from primitives with the same consensus number, but not all.

Findings

Objects with consensus number 1 have wait-free strongly-linearizable implementations from fetch&add.

Objects with consensus number 2 can have implementations from other objects with consensus number 2.

Some objects with consensus number 2, like queues and stacks, cannot have lock-free strongly-linearizable implementations even with primitives like fetch&add, swap, and test&set.

Abstract

A powerful tool for designing complex concurrent programs is through composition with object implementations from lower-level primitives. Strongly-linearizable implementations allow to preserve hyper-properties, e.g., probabilistic guarantees of randomized programs. However, the only known wait-free strongly-linearizable implementations for many objects rely on compare&swap, a universal primitive that allows any number of processes to solve consensus. This is despite the fact that these objects have wait-free linearizable implementations from read / write primitives, which do not support consensus. This paper investigates a middle-ground, asking whether there are wait-free strongly-linearizable implementations from realistic primitives such as test&set or fetch&add, whose consensus number is 2. We show that many objects with consensus number 1 have wait-free strongly-linearizable implementations from fetch&add. We also show that several objects with consensus number 2 have wait-free or lock-free implementations from other objects with consensus number 2. In contrast, we prove that even when fetch&add, swap and test&set primitives are used, some objects with consensus number 2 do not have lock-free strongly-linearizable implementations. This includes queues and stacks, as well as relaxed variants thereof.