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Silent Programmable Matter: Coating

Authors Alfredo Navarra , Francesco Piselli

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Author Details

Alfredo Navarra
  • Department of Mathematics and Computer Science, University of Perugia, Italy
Francesco Piselli
  • Department of Mathematics and Computer Science, University of Perugia, Italy

Funding

This work has been funded by the European Union - NextGenerationEU under the Italian Ministry of University and Research (MUR) National Innovation Ecosystem grant ECS00000041 - VITALITY - CUP J97G22000170005, and by the Italian National Group for Scientific Computation (GNCS-INdAM).

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Alfredo Navarra and Francesco Piselli. Silent Programmable Matter: Coating. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2023.25

Abstract

By Programmable Matter (PM) is usually meant a system of weak and self-organizing computational entities, called particles, which can be programmed via distributed algorithms to collectively achieve some global tasks. We consider the SILBOT model where particles are modeled as finite state automata, living and operating in the cells of a hexagonal grid. Particles are all identical, executing the same deterministic algorithm which is based on local observation of the surroundings, up to two hops. Particles are asynchronous, without any direct means of communication and disoriented but sharing a common handedness, i.e., chirality is assumed. Within such a basic model, we consider a foundational primitive for PM, that is Coating: a set of n particles must move so as to ensure the closed surrounding of an object occupying some connected cells of the grid. We present an optimal deterministic distributed algorithm - along with the correctness proof, that in Θ(n²) rounds solves the Coating problem, where a round concerns the minimal time window within which each particle is activated at least once.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Concurrency
  • Theory of computation → Self-organization
Keywords
  • Programmable Matter
  • Coating
  • Asynchrony
  • Stigmergy

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