CADbots：用有限自动机操纵可编程物质的数学方面
CADbots: Algorithmic Aspects of Manipulating Programmable Matter with Finite Automata
摘要：
我们贡献的结果，一组基本问题的背景下，可编程的物质，提出的算法方法，用于评估和操纵一个集体的粒子由一个有限自动机，既不能存储大量的数据，也不能执行复杂的计算，并限于少数可能的物理操作。我们提供了一个工具箱，用于在给定的瓷砖排列上执行基本任务，使用该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。具体的结果包括时间和空间效率的程序，用于绑定，计数，复制，反射，旋转或缩放复杂的给定形状。
英文摘要：
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 tiles, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
