We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store significant amounts of data, nor perform complex computations, and is limited to a handful of possible physical operations. We provide a toolbox for carrying out fundamental tasks on a given arrangement of particles, using the arrangement itself as a storage device, similar to a higher-dimensional Turing machine with geometric properties. Specific results include time- and space-efficient procedures for bounding, counting, copying, reflecting, rotating or scaling a complex given shape.

中文翻译：

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CADbots：使用有限自动机操作可编程物质的算法方面

我们通过提出算法方法来评估和操纵一组粒子的算法方法，该算法方法既不能存储大量数据，也不能执行复杂的计算，并且仅限于一个有限自动机。少数可能的物理操作。我们提供了一个工具箱，用于在给定的粒子排列上执行基本任务，使用排列本身作为存储设备，类似于具有几何特性的高维图灵机。具体结果包括对复杂的给定形状进行边界、计数、复制、反射、旋转或缩放的时间和空间效率高的程序。