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A Combinatorial Characterization of Self-stabilizing Population Protocols

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Stabilization, Safety, and Security of Distributed Systems (SSS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12514))

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Abstract

We characterize self-stabilizing functions in population protocols for complete interaction graphs. In particular, we investigate self-stabilization in systems of n finite state agents in which a malicious scheduler selects an arbitrary sequence of pairwise interactions under a global fairness condition. We show a necessary and sufficient condition for self-stabilization. Specifically we show that functions without certain set-theoretic conditions are impossible to compute in a self-stabilizing manner. Our main contribution is in the converse, where we construct a self-stabilizing protocol for all other functions that meet this characterization. Our positive construction uses Dickson’s Lemma to develop the notion of the root set, a concept that turns out to fundamentally characterize self-stabilization in this model. We believe it may lend to characterizing self-stabilization in more general models as well.

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Acknowledgments

We thank the anonymous reviewers for their helpful comments. This work is supported in part by DARPA under Cooperative Agreement No: HR0011-20-2-0025, NSF-BSF Grant 1619348, US-Israel BSF grant 2012366, Google Faculty Award, JP Morgan Faculty Award, IBM Faculty Research Award, Xerox Faculty Research Award, OKAWA Foundation Research Award, B. John Garrick Foundation Award, Teradata Research Award, and Lockheed-Martin Corporation Research Award. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, the Department of Defense, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes not withstanding any copyright annotation therein.

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Authors and Affiliations

  1. University of California, Los Angeles, USA

    Shaan Mathur & Rafail Ostrovsky

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  1. Shaan Mathur
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  2. Rafail Ostrovsky
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Correspondence to Shaan Mathur or Rafail Ostrovsky .

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Editors and Affiliations

  1. Grenoble Alpes University, Saint Martin d'Hères, France

    Stéphane Devismes

  2. The University of Texas at Austin, Richardson, TX, USA

    Neeraj Mittal

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Mathur, S., Ostrovsky, R. (2020). A Combinatorial Characterization of Self-stabilizing Population Protocols. In: Devismes, S., Mittal, N. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2020. Lecture Notes in Computer Science(), vol 12514. Springer, Cham. https://doi.org/10.1007/978-3-030-64348-5_13

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  • DOI: https://doi.org/10.1007/978-3-030-64348-5_13

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