Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space

Authors Philipp Czerner , Vincent Fischer , Roland Guttenberg



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Author Details

Philipp Czerner
  • Technical University of Munich, Germany
Vincent Fischer
  • Technical University of Munich, Germany
Roland Guttenberg
  • Technical University of Munich, Germany

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Philipp Czerner, Vincent Fischer, and Roland Guttenberg. Brief Announcement: The Expressive Power of Uniform Population Protocols with Logarithmic Space. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 44:1-44:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.44

Abstract

Population protocols are a model of computation in which indistinguishable mobile agents interact in pairs to decide a property of their initial configuration. Originally introduced by Angluin et. al. in 2004 with a constant number of states, research nowadays focuses on protocols where the space usage depends on the number of agents. The expressive power of population protocols has so far however only been determined for protocols using o(log n) states, which compute only semilinear predicates, and for Ω(n) states. This leaves a significant gap, particularly concerning protocols with Θ(log n) or Θ(polylog n) states, which are the most common constructions in the literature. In this paper we close the gap and prove that for any ε > 0 and f ∈ Ω(log n) ∩ 𝒪(n^{1-ε}), both uniform and non-uniform population protocols with Θ(f(n)) states can decide exactly NSPACE(f(n) log n).

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
Keywords
  • Population Protocols
  • Uniform
  • Expressive Power

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References

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