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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2016.7
URN: urn:nbn:de:0030-drops-70761
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7076/
Delporte-Gallet, Carole ;
Fauconnier, Hugues ;
Gafni, Eli ;
Kuznetsov, Petr
Set-Consensus Collections are Decidable
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.
BibTeX - Entry
@InProceedings{delportegallet_et_al:LIPIcs:2017:7076,
author = {Carole Delporte-Gallet and Hugues Fauconnier and Eli Gafni and Petr Kuznetsov},
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 = {Panagiota Fatourou and Ernesto Jim{\'e}nez and Fernando Pedone},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7076},
URN = {urn:nbn:de:0030-drops-70761},
doi = {10.4230/LIPIcs.OPODIS.2016.7},
annote = {Keywords: Decidability, distributed tasks, set consensus, Knapsack problem}
}
Keywords: |
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Decidability, distributed tasks, set consensus, Knapsack problem |
Collection: |
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20th International Conference on Principles of Distributed Systems (OPODIS 2016) |
Issue Date: |
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2017 |
Date of publication: |
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06.04.2017 |