Why Extension-Based Proofs Fail
Distributed, Parallel, and Cluster Computing
2020-08-04 v3
Abstract
We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve k-set agreement among n > k > 1 processes in a wait-free manner in certain asynchronous models. However, it was unknown whether proofs based on simpler techniques were possible. We show that this impossibility result cannot be obtained for one of these models by an extension-based proof and, hence, extension-based proofs are limited in power.
Cite
@article{arxiv.1811.01421,
title = {Why Extension-Based Proofs Fail},
author = {Dan Alistarh and James Aspnes and Faith Ellen and Rati Gelashvili and Leqi Zhu},
journal= {arXiv preprint arXiv:1811.01421},
year = {2020}
}
Comments
This version of the paper is for the NIS model. Previous versions of the paper are for the NIIS model