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 at 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. We first establish a set of sufficient conditions for algorithm correctness under any concurrent execution, embedding concurrency control directly in algorithm design. We then present a concurrency control framework 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. As a case study, we demonstrate both approaches using a simple algorithm for hexagon formation. Together, the canonical amoebot model and these complementary approaches to concurrent algorithm design open new directions for distributed computing research on programmable matter.

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，这些元素在本地交互以共同完成协调和移动任务。自从在 SPAA 2014 上推出以来，越来越多的文献对其假设进行了调整以解决各种问题；然而，如果没有标准化的假设层次结构，很难对变形虫模型下的结果进行精确的系统比较。我们提出了规范的 amoebot 模型，这是一种更新的形式化，可以区分核心模型特征和假设变体族。规范的 amoebot 模型解决的一个关键改进是并发性. 许多现有文献都隐含地假设变形虫动作是孤立且可靠的，从而将分析减少到一次最多有一个变形虫处于活动状态的顺序设置。然而，真正的可编程物质系统是并发的。规范的 amoebot 模型将所有 amoebot 通信形式化为消息传递，利用并发执行的对抗激活模型。在这种对时间的细粒度处理下，我们采用两种互补的方法来进行并发算法设计。我们首先建立了一组在任何并发执行下算法正确性的充分条件，将并发控制直接嵌入算法设计中。然后我们提出一个并发控制框架它使用锁将在顺序设置中终止并满足某些约定的 amoebot 算法转换为在并发设置中表现出等效行为的算法。作为案例研究，我们使用简单的六边形形成算法演示了这两种方法。规范的变形虫模型和这些并发算法设计的互补方法共同为可编程物质的分布式计算研究开辟了新方向。