Asynchronous Computability Theorem in Arbitrary Solo Models

• Main Authors: Yunguang Yue, Fengchun Lei, Xingwu Liu, Jie Wu
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Mathematics
• Subjects: distributed computing; asynchronous computability; solo model; solvability; combinatorial topology
• Online Access: https://www.mdpi.com/2227-7390/8/5/757

In this paper, we establish the asynchronous computability theorem in <i>d</i>-solo system by borrowing concepts from combinatorial topology, in which we state a necessary and sufficient conditions for a task to be wait-free computable in that system. Intuitively, a <i>d</i>-solo system allows as many <i>d</i> processes to access it as if each were running solo, namely, without detecting communication from any peer. As an application, we completely characterize the solvability of the input-less tasks in such systems. This characterization also leads to a hardness classification of these tasks according to whether their output complexes hold a <i>d</i>-nest structure. As a byproduct, we find an alternative way to distinguish the computational power of <i>d</i>-solo objects for different <i>d</i>.