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On the Number of Objects with Distinct Power and the Linearizability of Set Agreement Objects

Authors David Yu Cheng Chan, Vassos Hadzilacos, Sam Toueg



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David Yu Cheng Chan
Vassos Hadzilacos
Sam Toueg

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David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg. On the Number of Objects with Distinct Power and the Linearizability of Set Agreement Objects. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 12:1-12:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.DISC.2017.12

Abstract

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.
Keywords
  • Set Agreement
  • Asynchronous System
  • Shared Memory

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