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Brief Announcement: Solvability of Three-Process General Tasks

Authors Hagit Attiya , Pierre Fraigniaud , Ami Paz , Sergio Rajsbaum

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Author Details

Hagit Attiya
  • Department of Computer Science, Technion, Haifa, Israel
Pierre Fraigniaud
  • IRIF - CNRS & Université Paris Cité, France
Ami Paz
  • LISN - CNRS & Université Paris-Saclay, France
Sergio Rajsbaum
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico

Funding

  • Attiya, Hagit: partially supported by the Israel Science Foundation (22/1425).
  • Fraigniaud, Pierre: partially supported by the ANR projects DUCAT (ANR-20-CE48-0006), FREDDA (ANR-17-CE40-0013), and QuData (ANR-18-CE47-0010).
  • Rajsbaum, Sergio: Partially done while visiting IRIF-France and supported by the ANR project DUCAT (ANR-20-CE48-0006).

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Hagit Attiya, Pierre Fraigniaud, Ami Paz, and Sergio Rajsbaum. Brief Announcement: Solvability of Three-Process General Tasks. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 42:1-42:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.42

Abstract

The topological view on distributed computing represents a task T as a relation Δ between the complex ℐ of its inputs and the complex 𝒪 of its outputs. A cornerstone result in the field is an elegant computability characterization of the solvability of colorless tasks in terms of ℐ, 𝒪 and Δ. Essentially, a colorless task is wait-free solvable if and only if there is a continuous map from the geometric realization of ℐ to that of 𝒪 that respects Δ.
This paper makes headway towards providing an analogous characterization for general tasks, which are not necessarily colorless, by concentrating on the case of three-process inputless tasks. Our key contribution is identifying local articulation points as an obstacle for the solvability of general tasks, and defining a topological deformation on the output complex of a task T, which eliminates these points by splitting them, to obtain a new task T', with an adjusted relation Δ' between the input complex ℐ and an output complex 𝒪' without articulation points. We obtain a new characterization of wait-free solvability of three-process general tasks: T is wait-free solvable if and only if there is a continuous map from the geometric realization of ℐ to that of 𝒪' that respects Δ'.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Wait-free computing
  • lower bounds
  • topology

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