Synchronization power depends on the register size

Yehuda Afek*, Gideon Stupp

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Though it is common practice to treat synchronization primitives for multiprocessors as abstract data types, they are in reality machine instructions on registers. A crucial theoretical question with practical implications is the relationship between the size of the register and its computational power. We wish to study this question and choose as a first target the popular compare-&-swap operation (which is the basis for many modern multiprocessor architectures). Our main results are: 1. We show that multi-valued consensus among n processes can be solved using a compare&swap register that can hold ≈log n/log log n values. That is, n = (k-1)! where k is the number of values in the register, so the register has only O(log log n) bits. 2. We prove that there is a dependency between register size and processes' ability to solve multi-valued consensus. The key to the proof is a novel method of reducing a multi-valued decision task with limited size compare-&-swap registers to the set-consensus problem with read/write registers, allowing us to build on the recent powerful impossibility results of [2, 9, 18]. 3. We further use the reduction method to prove a tight tradeoff between the space and time necessary to solve multi-valued consensus with a compare-&-swap register. Specifically, we show that any algorithm for multi-valued consensus among n processes with a k value compare-&-swap register, where k≥log n/log log n, must have a run that accesses the register Θ (logk n) times. The results of this paper suggest that a complexity hierarchy for multiprocessor synchronization operations should be based on the space complexity of synchronization registers and not on the number of so called `synchronization objects.'

Original languageEnglish
Title of host publicationAnnual Symposium on Foundatons of Computer Science (Proceedings)
Editors Anon
PublisherPubl by IEEE
Number of pages10
ISBN (Print)0818643706
StatePublished - 1993
EventProceedings of the 34th Annual Symposium on Foundations of Computer Science - Palo Alto, CA, USA
Duration: 3 Nov 19935 Nov 1993

Publication series

NameAnnual Symposium on Foundatons of Computer Science (Proceedings)
ISSN (Print)0272-5428


ConferenceProceedings of the 34th Annual Symposium on Foundations of Computer Science
CityPalo Alto, CA, USA


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