The Computational Power of Distributed Shared-Memory Models with Bounded-Size Registers

TL;DR

This paper investigates whether distributed shared-memory models with bounded-size registers can match the computational power of models with unbounded registers, especially under crash failures, addressing fundamental questions of universality.

Contribution

It provides a characterization of the computational power of distributed shared-memory models with bounded-size registers, answering whether they are as powerful as unbounded ones under crash failures.

Findings

Bounded-size registers can simulate unbounded registers under certain conditions.

The model's universality depends on the number of process crashes.

The paper establishes conditions where bounded registers suffice for task solvability.

Abstract

The celebrated Asynchronous Computability Theorem of Herlihy and Shavit (STOC 1993 and STOC 1994) provided a topological characterization of the tasks that are solvable in a distributed system where processes are communicating by writing and reading shared registers, and where any number of processes can fail by crashing. However, this characterization assumes the use of full-information protocols, that is, protocols in which each time any of the processes writes in the shared memory, it communicates everything it learned since the beginning of the execution. Thus, the characterization implicitly assumes that each register in the shared memory is of unbounded size. Whether unbounded size registers are unavoidable for the model of computation to be universal is the central question studied in this paper. Specifically, is any task that is solvable using unbounded registers solvable using registers of bounded size? More generally, when at most $t$ processes can crash, is the model with bounded size registers universal? These are the questions answered in this paper.