Deterministic and Fast Randomized Test-and-Set in Optimal Space

TL;DR

This paper presents an optimal space deterministic implementation of test-and-set in shared memory systems and introduces a technique to convert obstruction-free algorithms into efficient randomized wait-free algorithms.

Contribution

It closes the gap between known bounds by providing a Theta(log n) register implementation and offers a method to transform obstruction-free algorithms into randomized wait-free ones.

Findings

Deterministic obstruction-free test-and-set uses Theta(log n) registers.

The transformation yields a randomized wait-free test-and-set with expected Theta(log* n) steps.

The approach bridges the gap between lower and upper bounds for register requirements.

Abstract

The test-and-set object is a fundamental synchronization primitive for shared memory systems. A test-and-set object stores a bit, initialized to 0, and supports one operation, test&set(), which sets the bit's value to 1 and returns its previous value. This paper studies the number of atomic registers required to implement a test-and-set object in the standard asynchronous shared memory model with n processes. The best lower bound is log(n)-1 for obstruction-free (Giakkoupis and Woelfel, 2012) and deadlock-free (Styer and Peterson, 1989) implementations. Recently a deterministic obstruction-free implementation using O(sqrt(n)) registers was presented (Giakkoupis, Helmi, Higham, and Woelfel, 2013). This paper closes the gap between these known upper and lower bounds by presenting a deterministic obstruction-free implementation of a test-and-set object from Theta(log n) registers of size Theta(log n) bits. We also provide a technique to transform any deterministic obstruction-free algorithm, in which, from any configuration, any process can finish if it runs for b steps without interference, into a randomized wait-free algorithm for the oblivious adversary, in which the expected step complexity is polynomial in n and b. This transformation allows us to combine our obstruction-free algorithm with the randomized test-and-set algorithm by Giakkoupis and Woelfel (2012), to obtain a randomized wait-free test-and-set algorithm from Theta(log n) registers, with expected step-complexity Theta(log* n) against the oblivious adversary.