The amoebot model [Derakhshandeh et al., 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., JCB 2022] of the geometric (variant of the) 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 some 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 then be used to solve the skeleton problem, where a (not necessarily simple) cycle of amoebots has to be found in the given amoebot structure which contains all boundary amoebots. A canonical solution to that problem can then 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 will then allow 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.
翻译:Amoebot 模型[Derakhshandeh 等人, 2014] 被提议为由小机器人元素组成的可编程物质的模型。 我们从一个小机器人元素组成的可编程物质的模型开始, 我们从一些基本问题入手, 比如条形计算问题, 如果考虑到任何连接的amobot 结构 $S$, 一个Amoebot 美元美元美元和一些轴 $X$, 所有的amobot 结构都可以通过所谓的电路连接 amoebot 。 一条电路允许连接的多条路之间的信号瞬间传输。 电路允许连接的多条路。 在本文中, 我们检查可重新配置的电路的电路结构结构的结构性能力。 直线计算方法可以让一个问题被使用到 $X $ 至 $ 美元 。 其次, 我们考虑全球最大问题, 在最高位置上找到一个可调序路路, 在某个给定的调序( 亚奥博) 的电路路路流结构中, 一定能将找到一个解到一个问题, 。 直流的解到一个解到直径结构的解到一个解到一个问题, 。