-set agreement requires a specific number of rounds based on the dimension of holes in the protocol complex.
Distributed Computing Through Combinatorial Topology (Book by Maurice Herlihy, Dmitry Kozlov, and Sergio Rajsbaum) distributed computing through combinatorial topology pdf
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Topologically, the protocol complex generated by a single round of immediate snapshots is a regular combinatorial subdivision of the input simplex. It is and, critically, contractible (it can be continuously shrunk to a single point without tearing or leaving holes). The Impossibility of Set Agreement distributed computing through combinatorial topology pdf