Immediate atomic snapshots and fast renaming
PODC '93 Proceedings of the twelfth annual ACM symposium on Principles of distributed computing
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Wait-free k-set agreement is impossible: the topology of public knowledge
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The asynchronous computability theorem for t-resilient tasks
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Unreliable failure detectors for reliable distributed systems
Journal of the ACM (JACM)
The weakest failure detector for solving consensus
Journal of the ACM (JACM)
The weakest failure detectors to solve certain fundamental problems in distributed computing
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Tight bounds for k-set agreement with limited-scope failure detectors
Distributed Computing - Special issue: DISC 03
On the weakest failure detector ever
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Anti-Ω: the weakest failure detector for set agreement
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
The weakest failure detector for solving k-set agreement
Proceedings of the 28th ACM symposium on Principles of distributed computing
The disagreement power of an adversary: extended abstract
Proceedings of the 28th ACM symposium on Principles of distributed computing
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
(anti-Ωx × Σz)-based k-set agreement algorithms
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
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In the k-set agreement task, n processes propose values, and have to decide on at most k of these values. In particular, consensus is 1-set agreement. In PODC 2008 Zieliński showed that the anti-Ω failure detector is necessary and sufficient to solve (n − 1)-set agreement in an asynchronous read/write shared memory system where at most n − 1 processes can fail by crashing. This paper generalizes Zieliński's result: it shows that anti-Ωt is the weakest failure detector to solve t-set agreement in a t-resilient asynchronous distributed system. Each query to antiΩt returns a set S of process ids, |S| = n − t, such that some correct process eventually never appears in any such set S; thus, anti-Ωn−1 = anti-Ω, and anti-Ω1 = Ω. Actually, the paper shows a stronger result: Any failure detector that can be used to solve T is at least as strong as anti-Ωt, for any agreement task T that has no t-resilient solution.