Early stopping in Byzantine agreement
Journal of the ACM (JACM)
Atomic snapshots of shared memory
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
More choices allow more faults: set consensus problems in totally asynchronous systems
Information and Computation
Impossibility of distributed consensus with one faulty process
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
Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
The topological structure of asynchronous computability
Journal of the ACM (JACM)
Long-lived and adaptive atomic snapshot and immediate snapshot (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Tight bounds for k-set agreement
Journal of the ACM (JACM)
The BG distributed simulation algorithm
Distributed Computing
Distributed Algorithms
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Uniform consensus is harder than consensus
Journal of Algorithms
Early deciding synchronous renaming in o( logf) rounds or less
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Brief announcement: pareto optimal solutions to consensus and set consensus
Proceedings of the 2013 ACM symposium on Principles of distributed computing
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In the $k$-set agreement problem, each processor starts with a private input value and eventually decides on an output value. At most $k$ distinct output values may be chosen, and every processor's output value must be one of the proposed values. We consider a synchronous message passing system, and we prove a tight bound of $\lfloor f/k\rfloor+2$ rounds of communication for all processors to decide in every run in which at most $f$ processors fail. The lower bound proof proceeds through a simulation of a synchronous solution to $k$-set agreement in message passing, in an asynchronous shared memory system in which $k-1$ processors may fail, and which was proven to be impossible using topological approaches. In contrast to past complexity results on set agreement, our lower bound proof is purely algorithmic. It does not use any direct topological argument but uses instead the impossibility of asynchronous set agreement to encapsulate the needed topology. We thus derive an adaptive complexity lower bound for a message passing system from a static impossibility in a shared memory system.