An algorithmic approach to the asynchronous computability theorem

An algorithmic approach to the asynchronous computability theorem 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 Herlihy and Shavit (Proceedings of the 25th annual ACM symposium on theory of computing, pp 111–120, 1993; J ACM 46(6):858–923, 1999) relied on an involved geometric argument. Borowsky and Gafni (Proceedings of the 16th annual ACM symposium on principles of distributed computing, pp 189–198, 1997) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Computational Topology Springer Journals

An algorithmic approach to the asynchronous computability theorem

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Algebraic Topology; Computational Science and Engineering; Mathematical and Computational Biology
ISSN
2367-1726
eISSN
2367-1734
D.O.I.
10.1007/s41468-018-0014-4
Publisher site
See Article on Publisher Site

Abstract

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 Herlihy and Shavit (Proceedings of the 25th annual ACM symposium on theory of computing, pp 111–120, 1993; J ACM 46(6):858–923, 1999) relied on an involved geometric argument. Borowsky and Gafni (Proceedings of the 16th annual ACM symposium on principles of distributed computing, pp 189–198, 1997) 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.

Journal

Journal of Applied and Computational TopologySpringer Journals

Published: May 29, 2018

References

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