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An algorithmic approach to the asynchronous computability theorem. (English) Zbl 1398.68372

Summary: The asynchronous computability theorem (ACT) uses concepts from combinatorial topology to characterize which tasks have wait-free solutions in read-write memory. A task can be expressed as a relation between two chromatic simplicial complexes. The theorem states that a task has a protocol (algorithm) if and only if there is a certain color-preserving simplicial map compatible with that relation. The original proof of the ACT, given by the second author and N. Shavit [in: Proceedings of the 25th annual ACM symposium on theory of computing, STOC’93. New York, NY: Association for Computing Machinery (ACM). 111–120 (1993; Zbl 1310.68079); J. ACM 46, No. 6, 858–923 (1999; Zbl 1161.68469)] relied on an involved geometric argument. E. Borowsky and the third author [in: Proceedings of the 16th annual ACM symposium on principles of distributed computing, PODC’97. New York, NY: Association for Computing Machinery (ACM). 189–198 (1997; Zbl 1374.68063)] later proposed an alternative proof based on a distributed algorithmic, termed the “convergence algorithm”. However the description of this algorithm was incomplete, and presented without proof. In this paper, we give the first complete description, along with a proof of correctness.

MSC:

68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
05E45 Combinatorial aspects of simplicial complexes
55U10 Simplicial sets and complexes in algebraic topology
68W15 Distributed algorithms
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References:

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