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Fault-tolerant simulation of population protocols

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Abstract

In this paper we investigate the computational power of population protocols under some unreliable or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the context of population protocols, is the loss by one or both parties of the information transmitted in an interaction. The failure may or may not be detected by either party. In one-way models, on the other hand, communication happens only in one direction: only one of the two agents can change its state depending on both agents’ states, and the other agent may or may not be aware of the interaction. These notions can be combined, obtaining one-way protocols with (possibly detectable) omission failures. We start our investigation by providing a complete classification of all the possible models arising from the aforementioned weaknesses, and establishing the computational hierarchy of these models. We then address for each model the fundamental question of what additional power is necessary and sufficient to completely overcome the model’s weakness and make it able to simulate faultless two-way protocols; by “simulator” we mean a wrapper protocol that, implementing an atomic communication of states between two agents, converts any standard two-way protocol into one that works in a weaker model. We answer this question by presenting simulators that work under certain assumptions (e.g., additional memory, unique IDs, etc.) and by proving that simulation is impossible without such assumptions.

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Acknowledgements

We would like to thank the anonymous reviewers for greatly improving the paper’s readability. This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada under the Discovery Grant program and by Prof. Flocchini’s University Research Chair.

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Authors and Affiliations

  1. LiS Laboratory, Aix-Marseille University, Campus de Luminy, 163 Avenue de Luminy, Marseille, France

    Giuseppe A. Di Luna

  2. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Avenue, Ottawa, ON, Canada

    Paola Flocchini

  3. Department of Computer Science and Engineering, Nagoya Institute of Technology, Gokisocho, Showa Ward, Nagoya, 466-8555, Japan

    Taisuke Izumi

  4. College of Information Science and Engineering, Ritsumeikan University, 56-1 Tojiin Kitamachi, Kita-ku, Kyoto, Japan

    Tomoko Izumi

  5. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada

    Nicola Santoro

  6. Jaist, 1-1 Asahidai, Nomi City, Ishikawa Prefecture, 923-1211, Japan

    Giovanni Viglietta

Authors
  1. Giuseppe A. Di Luna
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  2. Paola Flocchini
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  3. Taisuke Izumi
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  4. Tomoko Izumi
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  5. Nicola Santoro
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  6. Giovanni Viglietta
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Correspondence to Giovanni Viglietta.

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A preliminary version of this article has appeared in [25].

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Di Luna, G.A., Flocchini, P., Izumi, T. et al. Fault-tolerant simulation of population protocols. Distrib. Comput. 33, 561–578 (2020). https://doi.org/10.1007/s00446-020-00377-0

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  • DOI: https://doi.org/10.1007/s00446-020-00377-0

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