The amoebot model abstracts active programmable matter as a collection of simple computational elements called amoebots that interact locally to collectively achieve tasks of coordination and movement. Since its introduction (SPAA 2014), a growing body of literature has adapted its assumptions for a variety of problems; however, without a standardized hierarchy of assumptions, precise systematic comparison of results under the amoebot model is difficult. We propose the canonical amoebot model, an updated formalization that distinguishes between core model features and families of assumption variants. A key improvement addressed by the canonical amoebot model is concurrency. Much of the existing literature implicitly assumes amoebot actions are isolated and reliable, reducing analysis to the sequential setting where at most one amoebot is active at a time. However, real programmable matter systems are concurrent. The canonical amoebot model formalizes all amoebot communication as message passing, leveraging adversarial activation models of concurrent executions. Under this granular treatment of time, we take two complementary approaches to concurrent algorithm design. In the first, using hexagon formation as a case study, we establish a set of sufficient conditions that guarantee an algorithm's correctness under any concurrent execution, embedding concurrency control directly in algorithm design. In the second, we present a concurrency control protocol that uses locks to convert amoebot algorithms that terminate in the sequential setting and satisfy certain conventions into algorithms that exhibit equivalent behavior in the concurrent setting. These complementary approaches to concurrent algorithm design under the canonical amoebot model open new directions for distributed computing research on programmable matter and form a rigorous foundation for connections to related literature.

中文翻译：

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典范Amoebot模型：算法和并发控制

变形虫模型将活动的可编程物质抽象为称为变形虫的简单计算元素的集合，这些简单的计算元素在本地进行交互以共同完成协调和移动任务。自问世以来（SPAA，2014年），越来越多的文献针对各种问题调整了其假设。但是，如果没有标准化的假设层次结构，则难以在amoebot模型下对结果进行精确的系统比较。我们提出了经典的变形虫模型，这是一个更新的形式化模型，用于区分核心模型特征和假设变量系列。规范变形虫模型解决的一个关键改进是并发性。现有的许多文献都隐含地认为变形虫的动作是孤立且可靠的，将分析减少为一次最多可启动一个变形机器人的顺序设置。但是，真正的可编程系统是并发的。规范的变形虫模型将所有变形虫通信形式化为消息传递，并利用并发执行的对抗性激活模型。在这种细粒度的时间处理下，我们采用两种互补的方法进行并发算法设计。首先，以六角形形成为案例研究，我们建立了一组足以保证算法在任何并发执行下都正确的条件，并将并发控制直接嵌入算法设计中。在第二，我们提出了一种并发控制协议，该协议使用锁将终止于顺序设置并满足某些约定的变形机器人算法转换为在并发设置中表现出同等行为的算法。在典范变形虫模型下，这些并发算法设计的互补方法为可编程物质的分布式计算研究开辟了新的方向，并为与相关文献的连接奠定了严格的基础。