Task Solvability in Different Models
Abstract
The principal technical idea introduced in this chapter is a proof that if the single-layer complex is shellable, a combinatorial property defined later, multilayer compositions preserve connectivity under certain easily checkable conditions. These are theorems of combinatorial topology, independent of any model of computation.
We then show that for several models of computation that each single-layer complex is indeed shellable, so it becomes a straightforward exercise to derive tight (or nearly tight) bounds on when and if one can solve 
-set agreement.
Keywords
Asynchronous message-passing ...
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