|Title:||The Combinatorial Structure of Wait-free Solvable Tasks
|Authors:||Hagit Attiya and Sergio Rajsbaum
|Abstract:||This paper presents a self-contained study of wait-free solvable tasks. A new necessary and sufficient condition for wait-free solvability is proved, providing a characterization of the wait-free solvable tasks. The condition is based on a restricted set of executions, which induce a very simple to understand structure. The necessary condition is used to prove tight bounds for renaming and $k$-set consensus. The framework is based on topology, but uses only elementary combinatorics, and, in contrast to previous works, does not rely on algebraic or geometric arguments.|
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