Asynchronous Silent Programmable Matter: Line Formation

The paper discusses Programmable Matter (PM), where many small particles can change their physical properties in a controlled, programmable way. It focuses on a simplified PM reference model called SILBOT, where particles act asynchronously, cannot communicate directly, and do not remember past events. Within SILBOT, the authors study a specific task called Line Formation: particles must reach a final arrangement where they are aligned and connected. They propose a distributed algorithm designed to minimize the number of particle movements. The abstract states that the algorithm is accompanied by a correctness proof, supporting that it achieves the required aligned-and-connected configuration under the SILBOT constraints.