On the minimal synchronism needed for distributed consensus
Journal of the ACM (JACM)
Consensus in the presence of partial synchrony
Journal of the ACM (JACM)
Renaming in an asynchronous environment
Journal of the ACM (JACM)
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
More choices allow more faults: set consensus problems in totally asynchronous systems
Information and Computation
Distributed consensus revisited
Information Processing Letters
Sharing memory robustly in message-passing systems
Journal of the ACM (JACM)
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing
The weakest failure detector for solving consensus
Journal of the ACM (JACM)
Unifying synchronous and asynchronous message-passing models
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
A direct lower bound for k-set consensus
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
On k-set consensus problems in asynchronous systems
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
The Weak Byzantine Generals Problem
Journal of the ACM (JACM)
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
Distributed Algorithms
PODC '83 Proceedings of the second annual ACM symposium on Principles of distributed computing
Another advantage of free choice (Extended Abstract): Completely asynchronous agreement protocols
PODC '83 Proceedings of the second annual ACM symposium on Principles of distributed computing
Asynchronous Byzantine consensus
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
Efficient player-optimal protocols for strong and differential consensus
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Objects shared by Byzantine processes
Distributed Computing
The combined power of conditions and failure detectors to solve asynchronous set agreement
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Tight group renaming on groups of size g is equivalent to g-consensus
DISC'09 Proceedings of the 23rd international conference on Distributed computing
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In this paper, we investigate the k-set consensus problem in asynchronous distributed systems. In this problem, each participating process begins the protocol with an input value and by the end of the protocol must decide on one value so that at most k total values are decided by all correct processes. We extend previous work by exploring several variations of the problem definition and model, including for the first time investigation of Byzantine failures. We show that the precise definition of the validity requirement, which characterizes what decision values are allowed as a function of the input values and whether failures occur, is crucial to the solvability of the problem. For example, we show that allowing default decisions in case of failures makes the problem solvable for most values of k despite a minority of failures, even in face of the most severe type of failures (Byzantine). We introduce six validity conditions for this problem (all considered in various contexts in the literature), and demarcate the line between possible and impossible for each case. In many cases, this line is different from the one of the originally studied k-set consensus problem.