Asynchronous Silent Programmable Matter: Line Formation

TL;DR

This paper presents an optimal asynchronous silent algorithm for line formation in programmable matter, simplifying particle capabilities and ensuring correct alignment with minimal movements.

Contribution

It introduces a simple, optimal algorithm for line formation in SILBOT, addressing concurrency and capability limitations in programmable matter models.

Findings

Algorithm is proven correct.

Achieves line formation with minimal movements.

Works under asynchronous, silent, oblivious conditions.

Abstract

Programmable Matter (PM) has been widely investigated in recent years. It refers to some kind of matter with the ability to change its physical properties (e.g., shape or color) in a programmable way. One reference model is certainly Amoebot, with its recent canonical version (DISC 2021). Along this line, with the aim of simplification and to better address concurrency, the SILBOT model has been introduced (AAMAS 2020), which heavily reduces the available capabilities of the particles composing the PM. In SILBOT, in fact, particles are asynchronous, without any direct means of communication (silent) and without memory of past events (oblivious). Within SILBOT, we consider the Line Formation primitive in which particles are required to end up in a configuration where they are all aligned and connected. We propose a simple and elegant distributed algorithm - optimal in terms of number of movements, along with its correctness proof.