Agreement is harder than consensus: set consensus problems in totally asynchronous systems
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
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 BG distributed simulation algorithm
Distributed Computing
Using Failure Detectors to Solve Consensus in Asynchronous Sharde-Memory Systems (Extended Abstract)
WDAG '94 Proceedings of the 8th International Workshop on Distributed Algorithms
Anti-Ω: the weakest failure detector for set agreement
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Every problem has a weakest failure detector
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
(Almost) all objects are universal in message passing systems
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Automatic classification of eventual failure detectors
DISC'07 Proceedings of the 21st international conference on Distributed Computing
The multiplicative power of consensus numbers
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Turning adversaries into friends: simplified, made constructive, and extended
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
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We propose a complete characterization of a large class of distributed tasks, with respect to a weakened solvability notion called weak termination. A task is weak-termination solvable if there is an algorithm by which at least one process outputs. The proposed categorization of tasks is based on the weakest failure detectors needed to solve them. We show that every task T in the considered class is equivalent (in the failure detector sense) to some form of set agreement, and thus its solvability with weak termination is completely characterized by its set consensus number: the maximal integer k such that T can be (weak-termination) solved using read-write registers and k-set agreement objects. The characterization goes through showing that ¬Ωk, recently shown to be the weakest failure detector for the task of k-set agreement, is necessary to solve any task that is k-resilient impossible.