Motivated by the prospect of nano-robots that assist human physiological functions at the nanoscale, we investigate the coating problem in the three-dimensional model for hybrid programmable matter. In this model, a single agent with strictly limited viewing range and the computational capability of a deterministic finite automaton can act on passive tiles by picking up a tile, moving, and placing it at some spot. The goal of the coating problem is to fill each node of some surface graph of size n with a tile. We first solve the problem on a restricted class of graphs with a single tile type, and then use constantly many tile types to encode this graph in certain surface graphs capturing the surface of 3D objects. Our algorithm requires O(n2) steps, which is worst-case optimal compared to an agent with global knowledge and no memory restrictions.
@article{arxiv.2303.16180,
title = {Universal Coating by 3D Hybrid Programmable Matter},
author = {Irina Kostitsyna and David Liedtke and Christian Scheideler},
journal= {arXiv preprint arXiv:2303.16180},
year = {2024}
}