Topological Characterization of Consensus in Distributed Systems
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.
Cite
@article{arxiv.1905.09590,
title = {Topological Characterization of Consensus in Distributed Systems},
author = {Thomas Nowak and Ulrich Schmid and Kyrill Winkler},
journal= {arXiv preprint arXiv:1905.09590},
year = {2024}
}