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oai:drops-oai.dagstuhl.de:7997 2024-03-06T10:41:38Z ddc:004 open_access

On the Number of Objects with Distinct Power and the Linearizability of Set Agreement Objects Chan, David Yu Cheng Hadzilacos, Vassos Toueg, Sam Set Agreement Asynchronous System Shared Memory We first prove that there are uncountably many objects with distinct computational powers. More precisely, we show that there is an uncountable set of objects such that for any two of them, at least one cannot be implemented from the other (and registers) in a wait-free manner. We then strengthen this result by showing that there are uncountably many linearizable objects with distinct computational powers. To do so, we prove that for all positive integers n and k, there is a linearizable object that is computationally equivalent to the k-set agreement task among n processes. To the best of our knowledge, these are the first linearizable objects proven to be computationally equivalent to set agreement tasks. Schloss Dagstuhl – Leibniz-Zentrum für Informatik David Yu Cheng Chan and Vassos Hadzilacos and Sam Toueg 2017 Is Part Of LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2017.12 urn:nbn:de:0030-drops-79973 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.12 eng https://creativecommons.org/licenses/by/3.0/legalcode