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
Knowledge and common knowledge in a byzantine environment: crash failures
Information and Computation
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Set consensus using arbitrary objects (preliminary version)
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
A simple algorithmically reasoned characterization of wait-free computation (extended abstract)
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
The unified structure of consensus: a layered analysis approach
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
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
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
The topological structure of asynchronous computability
Journal of the ACM (JACM)
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge
SIAM Journal on Computing
Tight bounds for k-set agreement
Journal of the ACM (JACM)
Distributed computing: fundamentals, simulations and advanced topics
Distributed computing: fundamentals, simulations and advanced topics
Distributed Algorithms
The Combinatorial Structure of Wait-free Solvable Tasks (Extended Abstract)
WDAG '96 Proceedings of the 10th International Workshop on Distributed Algorithms
Polynomial algorithms for multiple processor agreement
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Mathematical Structures in Computer Science
Tight bounds for k-set agreement with limited-scope failure detectors
Distributed Computing - Special issue: DISC 03
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We have a new proof of the lower bound that k-set agreement requires 驴f/k驴 + 1 rounds in a synchronous, message-passing model with f crash failures. The proof involves constructing the set of reachable states, proving that these states are highly connected, and then appealing to a well-known topological result that high connectivity implies that set agreement is impossible. We construct the set of reachable states in an iterative fashion using a round operator that we define, and our proof of connectivity is an inductive proof based on this iterative construction and using simple properties of the round operator. This is the shortest and simplest proof of this lower bound we have seen.