eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-10-04
36:1
36:17
10.4230/LIPIcs.DISC.2021.36
article
Extension-Based Proofs for Synchronous Message Passing
Sheng, Yilun
1
Ellen, Faith
2
https://orcid.org/0000-0003-4473-931X
Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China
Department of Computer Science, University of Toronto, Canada
There is no wait-free algorithm that solves k-set agreement among n ≥ k+1 processes in asynchronous systems where processes communicate using only registers. However, proofs of this result for k ≥ 2 are complicated and involve topological reasoning. To explain why such sophisticated arguments are necessary, Alistarh, Aspnes, Ellen, Gelashvili, and Zhu recently introduced extension-based proofs, which generalize valency arguments, and proved that there are no extension-based proofs of this result.
In the synchronous message passing model, k-set agreement is solvable, but there is a lower bound of t rounds for any k-set agreement algorithm among n > kt processes when at most k processes can crash each round. The proof of this result for k ≥ 2 is also a complicated topological argument. We define a notion of extension-based proofs for this model and we show there are no extension-based proofs that t rounds are necessary for any k-set agreement algorithm among n = kt+1 processes, for k ≥ 2 and t > 2, when at most k processes can crash each round. In particular, our result shows that no valency argument can prove this lower bound.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol209-disc2021/LIPIcs.DISC.2021.36/LIPIcs.DISC.2021.36.pdf
Set agreement
lower bounds
valency arguments