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arXiv · 2303.14769

Colorless Tasks and Extension-Based Proofs

Yusong Shi·Weidong Liu
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Abstract

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 $n > k \geq 2$ 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.

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Yusong Shi, Weidong Liu. 2023-03-26. Colorless Tasks and Extension-Based Proofs. https://arxiv.org/abs/2303.14769

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