The amoebot model (Derakhshandeh et al. in: SPAA ACM, pp 220–222. https://doi.org/10.1145/2612669.2612712, 2014) has been proposed as a model for programmable matter consisting of tiny, robotic elements called amoebots. We consider the reconfigurable circuit extension (Feldmann et al. in J Comput Biol 29(4):317–343. https://doi.org/10.1089/cmb.2021.0363, 2022) of the geometric amoebot model that allows the amoebot structure to interconnect amoebots by so-called circuits. A circuit permits the instantaneous transmission of signals between the connected amoebots. In this paper, we examine the structural power of the reconfigurable circuits. We start with fundamental problems like the stripe computation problem where, given any connected amoebot structure S, an amoebot u in S, and some axis X, all amoebots belonging to axis X through u have to be identified. Second, we consider the global maximum problem, which identifies an amoebot at the highest possible position with respect to some direction in some given amoebot (sub)structure. A solution to this problem can be used to solve the skeleton problem, where a cycle of amoebots has to be found in the given amoebot structure which contains all boundary amoebots. A canonical solution to that problem can be used to come up with a canonical path, which provides a unique characterization of the shape of the given amoebot structure. Constructing canonical paths for different directions allows the amoebots to set up a spanning tree and to check symmetry properties of the given amoebot structure. The problems are important for a number of applications like rapid shape transformation, energy dissemination, and structural monitoring. Interestingly, the reconfigurable circuit extension allows polylogarithmic-time solutions to all of these problems.

amoebot 模型（Derakhshandeh 等人，见：SPAA ACM，第 220-222 页。https://doi.org/10.1145/2612669.2612712，2014）已被提议作为由称为amoebots的微小机器人元件组成的可编程物质的模型。我们考虑几何 amoebot 模型的可重构电路扩展（Feldmann et al. in J Comput Biol 29(4):317–343. https://doi.org/10.1089/cmb.2021.0363, 2022），该模型允许 amoebot 结构通过所谓的电路互连amoebots 。电路允许在连接的amoebots之间即时传输信号。在本文中，我们研究了可重构电路的结构能力。我们从基本问题开始，例如条带计算问题，其中给定任何连接的 amoebot 结构S 、 S中的amoebot u和某个轴X ，必须识别属于X轴到u的所有 amoebot。其次，我们考虑全局最大值问题，它在某个给定的 amoebot（子）结构中相对于某个方向识别处于最高可能位置的 amoebot。该问题的解决方案可用于解决骨架问题，其中必须在给定的包含所有边界 amoebot 的 amoebot 结构中找到 amoebot 的循环。该问题的规范解决方案可用于提出规范路径，该路径提供给定 amoebot 结构形状的独特特征。构建不同方向的规范路径允许 amoebot 建立生成树并检查给定 amoebot 结构的对称性。这些问题对于快速形状变换、能量传播和结构监测等许多应用都很重要。有趣的是，可重构电路扩展允许对所有这些问题进行多对数时间解决方案。