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A General Input-Dependent Colorless Computability Theorem and Applications to Core-Dependent Adversaries

Authors Yannis Coutouly , Emmanuel Godard

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LIPIcs.OPODIS.2025.13.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Computability
Keywords
  • colorless task
  • topological methods
  • geometric simplicial complex
  • k-set-agreement
  • t-resilient model
  • condition-based computability

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Abstract

Distributed computing tasks can be presented with a triple (ℐ,𝒪,Δ). The solvability of a colorless task on the Iterated Immediate Snapshot model (IIS) has been characterized by the Colorless Computability Theorem [Maurice Herlihy et al., 2013]. A recent paper [Yannis Coutouly and Emmanuel Godard, 2024] generalizes this theorem for any message adversaries ℳ ⊆ IIS by geometric methods.
In 2001, Mostéfaoui, Rajsbaum, Raynal, and Roy [Achour Mostéfaoui et al., 2002] introduced condition-based adversaries. This setting considers a particular adversary that will be applied only to a subset of input configurations. In this setting, they studied the k-set agreement task with condition-based t-resilient adversaries and obtained a sufficient condition on the conditions that make k-Set Agreement solvable.
In this paper we have three contributions:  
1) We generalize the characterization of [Yannis Coutouly and Emmanuel Godard, 2024] to input-dependent adversaries, which means that the adversaries can change depending on the input configuration. 
2) We show that core-resilient adversaries of IIS_n have the same computability power as the core-resilient adversaries of IIS_n where crashes only happen at the start. 
3) Using the two previous contributions, we provide a necessary and sufficient characterization of the condition-based, core-dependent adversaries that can solve k-Set Agreement. 
We also distinguish four settings that may appear when presenting a distributed task as (ℐ,𝒪,Δ). Finally, in a later section, we present structural properties on the carrier map Δ. Such properties allow simpler proof, without changing the computability power of the task. Most of the proofs in this article leverage the topological framework used in distributed computing by using simple geometric constructions.

Cite As Get BibTex

Yannis Coutouly and Emmanuel Godard. A General Input-Dependent Colorless Computability Theorem and Applications to Core-Dependent Adversaries. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.OPODIS.2025.13

Author Details

Yannis Coutouly
  • Aix-Marseille University, CNRS LIS UMR7020, Marseille, France
Emmanuel Godard
  • Aix-Marseille University, CNRS LIS UMR7020, Marseille, France

Funding

This work was partially supported by DUCAT (Distributed Network Computing through the Lens of Combinatorial Topology - France ANR-20-CE48-0006).

Acknowledgements

The authors wish to sincerely thank Sergio Rajsbaum for suggesting condition-based computability as an application of [Yannis Coutouly and Emmanuel Godard, 2024].

References

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