Time and space lower bounds for non-blocking implementations

Abstract

We show the following time and space complexity lower bounds. Let I be any randomized non-blocking n-process implementation of any object in set A from any combination of objects in set B, where A = {increment, store-conditional bit, compare & swap, bounded-counter, single-writer atomic snapshot, fetch & add}, and B = {resettable consensus, register, swap register}. The space complexity of I is at least n - 1. Moreover, if I is deterministic, both its time and space complexity are at least n - 1. These lower bounds hold even if objects used in the implementation are of unbounded size. This improves on some of the Ω(√n) space complexity lower bounds of Fich, Herlihy & Shavit [FHS93]. It also shows the near optimality of some known wait-free implementations in terms of space complexity.