License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2019.16
URN: urn:nbn:de:0030-drops-118026
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11802/
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de Azevedo Piovezan, Felipe ; Hadzilacos, Vassos ; Toueg, Sam

On Deterministic Linearizable Set Agreement Objects

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LIPIcs-OPODIS-2019-16.pdf (0.8 MB)


Abstract

A recent work showed that, for all n and k, there is a linearizable (n,k)-set agreement object O_L that is equivalent to the (n,k)-set agreement task [David Yu Cheng Chan et al., 2017]: given O_L, it is possible to solve the (n,k)-set agreement task, and given any algorithm that solves the (n,k)-set agreement task (and registers), it is possible to implement O_L. This linearizable object O_L, however, is not deterministic. It turns out that there is also a deterministic (n,k)-set agreement object O_D that is equivalent to the (n,k)-set agreement task, but this deterministic object O_D is not linearizable. This raises the question whether there exists a deterministic and linearizable (n,k)-set agreement object that is equivalent to the (n,k)-set agreement task. Here we show that in general the answer is no: specifically, we prove that for all n ≥ 4, every deterministic linearizable (n,2)-set agreement object is strictly stronger than the (n,2)-set agreement task. We prove this by showing that, for all n ≥ 4, every deterministic and linearizable (n,2)-set agreement object (together with registers) can be used to solve 2-consensus, whereas it is known that the (n,2)-set agreement task cannot do so. For a natural subset of (n,2)-set agreement objects, we prove that this result holds even for n = 3.

BibTeX - Entry

@InProceedings{deazevedopiovezan_et_al:LIPIcs:2020:11802,
  author =	{Felipe de Azevedo Piovezan and Vassos Hadzilacos and Sam Toueg},
  title =	{{On Deterministic Linearizable Set Agreement Objects}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Pascal Felber and Roy Friedman and Seth Gilbert and Avery Miller},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11802},
  URN =		{urn:nbn:de:0030-drops-118026},
  doi =		{10.4230/LIPIcs.OPODIS.2019.16},
  annote =	{Keywords: Asynchronous shared-memory systems, consensus, set agreement, deterministic objects}
}

Keywords: Asynchronous shared-memory systems, consensus, set agreement, deterministic objects
Collection: 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)
Issue Date: 2020
Date of publication: 11.02.2020


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