We study models and algorithms for Programmable Matter (PM), that is matter with the ability to change its physical properties (e.g., shape or optical properties) in a programmable fashion. PM can be implemented by assembling a system of weak self-organizing computational elements, called particles, that can be programmed via distributed algorithms to collectively achieve some global task. Recent advances in the production of nanotechnologies have rendered such systems increasingly possible in practice, thus triggering research interests from many areas of computer science. The most established models for PM assume that particles: are modeled as finite state automata; are all identical, executing the same algorithm based on local observation of the surroundings; live and operate in the cells of a hexagonal grid; can move from one cell to another by repeatedly alternating between a contracted state (a particle occupies one cell) and an expanded state (a particle occupies two neighboring cells). Given these elementary features, it is rather hard to design distributed algorithms even for basic tasks and, in fact, all existing solutions to solve fundamental problems via PM have resorted to endowing PM systems with various capabilities to overcome such hardness, thus assuming quite unrealistic features. In this paper, we move toward more realistic computational models for PM. Specifically, we first introduce ${\sf SILBOT}$ , a new modeling approach that relaxes several assumptions used in previous ones. Second, we present a distributed algorithm to solve, in the ${\sf SILBOT}$ model, a foundational primitive for PM, namely Leader Election. This algorithm works in $O(n)$ rounds for all initial configurations of $n$ particles that are both connected (i.e. particles induce a connected graph) and compact (i.e. without holes, that is no empty cells surrounded by particles occur). As usual in asynchronous contexts, a round is intended as the time within which all particles have been activated at least once. Third, we show that, if the initial configuration admits holes, it is impossible to achieve leader election while preserving connectivity. Finally, by slightly empowering the robots, we design an algorithm to handle initial configurations admitting holes that in $O(n^{2})$ rounds solves the leader election problem while obtaining also compaction.

中文翻译：

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异步无声可编程物质实现leader选举和压实

我们研究模型和算法 可编程物质(PM)，即具有以可编程方式改变其物理特性（例如，形状或光学特性）的能力的物质。PM 可以通过组装一个弱自组织计算元素系统来实现，称为粒子，可以通过分布式算法进行编程以共同完成一些全局任务。纳米技术生产的最新进展使这种系统在实践中越来越成为可能，从而引发了计算机科学许多领域的研究兴趣。最成熟的 PM 模型假设粒子： 被建模为有限状态自动机；都是相同的，基于对周围环境的局部观察执行相同的算法；在六边形网格的单元格中生活和运作；可以通过在一个单元格之间反复交替来从一个单元格移动到另一个单元格签约 状态（一个粒子占据一个细胞）和一个 展开状态（一个粒子占据两个相邻的单元格）。鉴于这些基本特征，即使是基本任务也很难设计分布式算法，事实上，所有通过 PM 解决基本问题的现有解决方案都诉诸于赋予 PM 系统各种能力来克服这种困难，从而假设了非常不切实际的特征. 在本文中，我们转向更现实的 PM 计算模型。具体来说，我们首先介绍 ${\sf SILBOT}$ ，一种新的建模方法，它放宽了以前使用的几个假设。其次，我们提出了一个分布式算法来解决，在 ${\sf SILBOT}$ 模型，PM 的基本原语，即 领袖选举. 该算法适用于 $O(n)$ 所有初始配置的轮次 $n$ 两者都是粒子 连接的 （即粒子诱导连通图）和 袖珍的 （即没有 洞，即不会出现被粒子包围的空单元）。像往常一样在异步上下文中，一个圆形的是指所有粒子至少被激活一次的时间。第三，我们表明，如果初始配置允许漏洞，则不可能在保持连通性的同时实现领导者选举。最后，通过稍微授权机器人，我们设计了一种算法来处理初始配置，允许在 $O(n^{2})$ rounds 解决了领导者选举问题，同时也获得了压缩。