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Article

Asynchronous Computability Theorem in Arbitrary Solo Models

by
Yunguang Yue
1,†,
Fengchun Lei
1,*,†,
Xingwu Liu
1,2,3,† and
Jie Wu
4,†
1
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2
SKL Computer Architecture, ICT, CAS, Beijing 100049, China
3
School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
4
College of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2020, 8(5), 757; https://doi.org/10.3390/math8050757
Submission received: 2 March 2020 / Revised: 24 April 2020 / Accepted: 29 April 2020 / Published: 10 May 2020
(This article belongs to the Section E1: Mathematics and Computer Science)
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Abstract

In this paper, we establish the asynchronous computability theorem in d-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 d-solo system allows as many d 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 d-nest structure. As a byproduct, we find an alternative way to distinguish the computational power of d-solo objects for different d.
Keywords: distributed computing; asynchronous computability; solo model; solvability; combinatorial topology distributed computing; asynchronous computability; solo model; solvability; combinatorial topology

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MDPI and ACS Style

Yue, Y.; Lei, F.; Liu, X.; Wu, J. Asynchronous Computability Theorem in Arbitrary Solo Models. Mathematics 2020, 8, 757. https://doi.org/10.3390/math8050757

AMA Style

Yue Y, Lei F, Liu X, Wu J. Asynchronous Computability Theorem in Arbitrary Solo Models. Mathematics. 2020; 8(5):757. https://doi.org/10.3390/math8050757

Chicago/Turabian Style

Yue, Yunguang, Fengchun Lei, Xingwu Liu, and Jie Wu. 2020. "Asynchronous Computability Theorem in Arbitrary Solo Models" Mathematics 8, no. 5: 757. https://doi.org/10.3390/math8050757

APA Style

Yue, Y., Lei, F., Liu, X., & Wu, J. (2020). Asynchronous Computability Theorem in Arbitrary Solo Models. Mathematics, 8(5), 757. https://doi.org/10.3390/math8050757

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