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On Set Consensus Numbers
Citation key GK-OSCN-09
Author Gafni, Eli and Kuznetsov, Petr
Title of Book Distributed Computing (Proceedings of the 23rd International Symposium on Distributed Computing (DISC 2009))
Pages 35–47
Year 2009
ISBN 978-3-642-04354-3
ISSN 0302-9743
DOI http://dx.doi.org/10.1007/978-3-642-04355-0_8
Location Elche/Elx, Spain
Address Berlin / Heidelberg
Month September
Note nominated for Best Paper Award
Publisher Springer
Abstract We propose a complete characterization of a large class of distributed tasks, with respect to a weakened solvability notion called it weak termination. A task is weak-termination solvable if there is an algorithm by which at least one process outputs. The proposed categorization of tasks is based on the weakest failure detectors needed to solve them. We show that every task T in the considered class is equivalent (in the failure detector sense) to some form of set agreement, and thus its solvability with weak termination is completely characterized by its set consensus number: the maximal integer K such that T can be (weak-termination) solved using read-write registers and k-set agreement objects. The characterization goes through showing that ¬Ω_k, recently shown to be the weakest failure detector for the task of k-set agreement, is necessary to solve any task that is k-resilient impossible.
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