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Simultaneous Consensus is Harder than Set Agreement in Message Passing

Abstract : In the traditional consensus task, processes are required to agree on a common value chosen among the initial values of the participants. It is well known that consensus cannot be solved in crashed-prone, asynchronous distributed systems. Two generalizations of the consensus problem have been introduced: k-set agreement and k-simultaneous consensus. The k-set agreement task has the same requirements as consensus except that processes are allowed to decide up to k distinct values. In the k-simultaneous consensus task, each process participates simultaneously in k instances of consensus and is required to decide in at least one of them; any two processes deciding in the same instance must decide the same value. It is known that both tasks are equivalent in the wait-free shared memory model. Perhaps surprisingly, the paper shows that this is no longer the case in the n-process asynchronous message passing model with at most t process crashes. Specifically, the paper establishes that for parameters t, n, k such that t > (n+k−2)/2 , k-simultaneous consensus is strictly harder than k-set agreement. The proof compares the information on failures necessary to solve each task in the failure detector framework and relies on a result in topological combinatorics, namely, the chromatic number of Kneser graphs. The paper also introduces the new failure detector class V Σk , which is a generalization of the quorum failures detector class Σ suited to k-simultaneous consensus.
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Contributor : Corentin Travers <>
Submitted on : Friday, November 16, 2012 - 10:40:46 AM
Last modification on : Friday, August 31, 2018 - 9:25:53 AM
Document(s) archivé(s) le : Saturday, December 17, 2016 - 11:30:02 AM


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  • HAL Id : hal-00752610, version 1


Zohir Bouzid, Corentin Travers. Simultaneous Consensus is Harder than Set Agreement in Message Passing. 2012. ⟨hal-00752610v1⟩



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