Topological Characterization of Consensus in Distributed Systems

Thomas Nowak; Ulrich Schmid; Kyrill Winkler

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arXiv · 1905.09590

Topological Characterization of Consensus in Distributed Systems

Thomas Nowak·Ulrich Schmid·Kyrill Winkler

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Abstract

We provide a complete characterization of both uniform and non-uniform deterministic consensus solvability in distributed systems with benign process and communication faults using point-set topology. More specifically, we non-trivially extend the approach introduced by Alpern and Schneider in 1985, by introducing novel fault-aware topologies on the space of infinite executions: the process-view topology, induced by a distance function that relies on the local view of a given process in an execution, and the minimum topology, which is induced by a distance function that focuses on the local view of the process that is the last to distinguish two executions. Consensus is solvable in a given model if and only if the sets of admissible executions leading to different decision values is disconnected in these topologies. By applying our approach to a wide range of different applications, we provide a topological explanation of a number of existing algorithms and impossibility results and develop several new ones, including a general equivalence of the strong and weak validity conditions.

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BibTeX RIS

Thomas Nowak, Ulrich Schmid, Kyrill Winkler. 2019-05-23. Topological Characterization of Consensus in Distributed Systems. https://arxiv.org/abs/1905.09590

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