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Asynchronous Computability Theorem in Arbitrary Solo Models

Author

Listed:
  • Yunguang Yue

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
    These authors contributed equally to this work.)

  • Fengchun Lei

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
    These authors contributed equally to this work.)

  • Xingwu Liu

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
    SKL Computer Architecture, ICT, CAS, Beijing 100049, China
    School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
    These authors contributed equally to this work.)

  • Jie Wu

    (College of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    These authors contributed equally to this work.)

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 .

Suggested Citation

  • Yunguang Yue & Fengchun Lei & Xingwu Liu & Jie Wu, 2020. "Asynchronous Computability Theorem in Arbitrary Solo Models," Mathematics, MDPI, vol. 8(5), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:757-:d:356120
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    Cited by:

    1. Yunguang Yue & Xingwu Liu & Fengchun Lei & Jie Wu, 2022. "A Topological Characterization to Arbitrary Resilient Asynchronous Complexity," Mathematics, MDPI, vol. 10(15), pages 1-20, August.

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