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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.2020.18
URN: urn:nbn:de:0030-drops-135037
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13503/
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Attiya, Hagit ; Castañeda, Armando ; Rajsbaum, Sergio

Locally Solvable Tasks and the Limitations of Valency Arguments

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LIPIcs-OPODIS-2020-18.pdf (1 MB)

Abstract

An elegant strategy for proving impossibility results in distributed computing was introduced in the celebrated FLP consensus impossibility proof. This strategy is local in nature as at each stage, one configuration of a hypothetical protocol for consensus is considered, together with future valencies of possible extensions. This proof strategy has been used in numerous situations related to consensus, leading one to wonder why it has not been used in impossibility results of two other well-known tasks: set agreement and renaming. This paper provides an explanation of why impossibility proofs of these tasks have been of a global nature. It shows that a protocol can always solve such tasks locally, in the following sense. Given a configuration and all its future valencies, if a single successor configuration is selected, then the protocol can reveal all decisions in this branch of executions, satisfying the task specification. This result is shown for both set agreement and renaming, implying that there are no local impossibility proofs for these tasks.

BibTeX - Entry

@InProceedings{attiya_et_al:LIPIcs:2021:13503,
  author =	{Hagit Attiya and Armando Casta{\~n}eda and Sergio Rajsbaum},
  title =	{{Locally Solvable Tasks and the Limitations of Valency Arguments}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Quentin Bramas and Rotem Oshman and Paolo Romano},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13503},
  URN =		{urn:nbn:de:0030-drops-135037},
  doi =		{10.4230/LIPIcs.OPODIS.2020.18},
  annote =	{Keywords: Wait-freedom, Set agreement, Weak symmetry breaking, Impossibility proofs}
}

Keywords: Wait-freedom, Set agreement, Weak symmetry breaking, Impossibility proofs
Collection: 24th International Conference on Principles of Distributed Systems (OPODIS 2020)
Issue Date: 2021
Date of publication: 25.01.2021

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