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DOI: 10.4230/LIPIcs.OPODIS.2016.7

Set-Consensus Collections are Decidable

Authors: Carole Delporte-Gallet, Hugues Fauconnier, Eli Gafni, and Petr Kuznetsov

Published in: LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)

Abstract

A natural way to measure the power of a distributed-computing model is to characterize the set of tasks that can be solved in it. In general, however, the question of whether a given task can be solved in a given model is undecidable, even if we only consider the wait-free shared-memory model. In this paper, we address this question for restricted classes of models and tasks. We show that the question of whether a collection C of (l, j)-set consensus objects, for various l (the number of processes that can invoke the object) and j (the number of distinct outputs the object returns), can be used by n processes to solve wait-free k-set consensus is decidable. Moreover, we provide a simple O(n^2) decision algorithm, based on a dynamic programming solution to the Knapsack optimization problem. We then present an adaptive wait-free set-consensus algorithm that, for each set of participating processes, achieves the best level of agreement that is possible to achieve using C. Overall, this gives us a complete characterization of a read-write model defined by a collection of set-consensus objects through its set-consensus power.

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Carole Delporte-Gallet, Hugues Fauconnier, Eli Gafni, and Petr Kuznetsov. Set-Consensus Collections are Decidable. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{delportegallet_et_al:LIPIcs.OPODIS.2016.7,
  author =	{Delporte-Gallet, Carole and Fauconnier, Hugues and Gafni, Eli and Kuznetsov, Petr},
  title =	{{Set-Consensus Collections are Decidable}},
  booktitle =	{20th International Conference on Principles of Distributed Systems (OPODIS 2016)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-031-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{70},
  editor =	{Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.7},
  URN =		{urn:nbn:de:0030-drops-70761},
  doi =		{10.4230/LIPIcs.OPODIS.2016.7},
  annote =	{Keywords: Decidability, distributed tasks, set consensus, Knapsack problem}
}

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Set-Consensus Collections are Decidable

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