The concept of extension-based proofs models the idea of a valency argument, which is widely used in distributed computing. Extension-based proofs are limited in power: it has been shown that there is no extension-based proof of the impossibility of a wait-free protocol for (n,k)-set agreement among n>k≥2 processes. There are only a few tasks that have been proven to have no extension-based proof of the impossibility, since the techniques in these works are closely related to the specific task. We give a necessary and sufficient condition for colorless tasks to have no extension-based proofs of the impossibility of wait-free protocols in the NIIS model. We introduce a general adversarial strategy decoupled from any concrete task specification. In this strategy, some properties of the chromatic subdivision that is widely used in distributed computing are proved.
@article{arxiv.2303.14769,
title = {Colorless Tasks and Extension-Based Proofs},
author = {Yusong Shi and Weidong Liu},
journal= {arXiv preprint arXiv:2303.14769},
year = {2024}
}