A necessary condition for Byzantine k-set agreement

•A simple necessity proof for k-set agreement.•It answers a computability issue.•The proof covers synchronous and asynchronous systems. This short paper presents a necessary condition for Byzantine k-set agreement in (synchronous or asynchronous) message-passing systems and asynchronous shared memor...

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Bibliographic Details
Published in:Information processing letters 2016-12, Vol.116 (12), p.757-759
Main Authors: Bouzid, Zohir, Imbs, Damien, Raynal, Michel
Format: Article
Language:English
Subjects:
Algorithms
Asynchronous
Atomic read/write register
Byzantine process
Computer memory
Geometry
Information processing
k-Set agreement
Message-passing system
Studies
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Summary:•A simple necessity proof for k-set agreement.•It answers a computability issue.•The proof covers synchronous and asynchronous systems. This short paper presents a necessary condition for Byzantine k-set agreement in (synchronous or asynchronous) message-passing systems and asynchronous shared memory systems where the processes communicate through atomic single-writer multi-reader registers. It gives a proof, which is particularly simple, that k-set agreement cannot be solved t-resiliently in an n-process system when n≤2t+tk. This bound is tight for the case k=1 (Byzantine consensus) in synchronous message-passing systems.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2016.06.009