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The asynchronous computability theorem (ACT) uses concepts from combinatorialtopology to characterize which tasks have wait-free solutions in read-writememory. A task can be expressed as a relation between two chromatic simplicialcomplexes. The theorem states that a task has a protocol (algorithm) if andonly if there is a certain chromatic simplicial map compatible with thatrelation.  While the original proof of the ACT relied on an involved combinatorialargument, Borowsky and Gafni later proposed an alternative proof that relied ona algorithmic construction, termed the "convergence algorithm". The descriptionof this algorithm was incomplete, and presented without proof. In this paper,we give the first complete description, along with a proof of correctness.

An Algorithmic Approach to the Asynchronous Computability Theorem