Fully Dynamic Line Maintenance by Hybrid Programmable Matter

Motivated by the manipulation of nanoscale materials, recent investigations have focused on hybrid systems where passive elements incapable of movement, called tiles, are manipulated by one or more mobile entities, called robots, with limited computational capabilities. Like in most self-organizing systems, the fundamental concern is with the (geometric) shapes created by the position of the tiles; among them, the line is perhaps the most important. The existing investigations have focused on formation of the shape, but not on its reconfiguration following the failure of some of the tiles. In this paper, we study the problem of maintaining a line formation in presence of fully dynamic failures: any tile can stop functioning at any time. We show how this problem can be solved by a group of very simple robots, with the computational power of deterministic finite automata.