Distributed Computation with Continual Population Growth

Authors Da-Jung Cho , Matthias Függer , Corbin Hopper , Manish Kushwaha , Thomas Nowak , Quentin Soubeyran

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Da-Jung Cho
  • University of Kassel, Germany
Matthias Függer
  • CNRS, LSV, ENS Paris-Saclay, Université Paris-Saclay, Inria, Gif-sur-Yvette, France
Corbin Hopper
  • ENS Paris-Saclay, Gif-sur-Yvette, France
  • Université Paris-Saclay, CNRS, Orsay, France
Manish Kushwaha
  • Université Paris-Saclay, INRAE, AgroParisTech, Micalis Institute, Jouy-en-Josas, France
Thomas Nowak
  • Université Paris-Saclay, CNRS, Orsay, France
Quentin Soubeyran
  • École polytechnique, Institut Polytechnique de Paris, Route de Saclay, Palaiseau, France
  • Université Paris-Saclay, CNRS, Orsay, France


We acknowledge support from the Digicosme working group HicDiesMeus, Ile-de-France region’s DIM-RFSI, INRAE’s MICA department, and the CNRS project ABIDE. We thank Joel Rybicki for feedback on an earlier version.

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Da-Jung Cho, Matthias Függer, Corbin Hopper, Manish Kushwaha, Thomas Nowak, and Quentin Soubeyran. Distributed Computation with Continual Population Growth. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Computing with synthetically engineered bacteria is a vibrant and active field with numerous applications in bio-production, bio-sensing, and medicine. Motivated by the lack of robustness and by resource limitation inside single cells, distributed approaches with communication among bacteria have recently gained in interest. In this paper, we focus on the problem of population growth happening concurrently, and possibly interfering, with the desired bio-computation. Specifically, we present a fast protocol in systems with continuous population growth for the majority consensus problem and prove that it correctly identifies the initial majority among two inputs with high probability if the initial difference is Ω(√{nlog n}) where n is the total initial population. We also present a fast protocol that correctly computes the NAND of two inputs with high probability. We demonstrate that combining the NAND gate protocol with the continuous-growth majority consensus protocol, using the latter as an amplifier, it is possible to implement circuits computing arbitrary Boolean functions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • microbiological circuits
  • majority consensus
  • birth-death processes


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