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arXiv · 1810.06360

CADbots: Algorithmic Aspects of Manipulating Programmable Matter with Finite Automata

Sándor P. Fekete·Robert Gmyr·Sabrina Hugo·Phillip Keldenich·Christian Scheffer·Arne Schmidt
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Abstract

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.

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Sándor P. Fekete, Robert Gmyr, Sabrina Hugo, Phillip Keldenich, Christian Scheffer, Arne Schmidt. 2018-10-15. CADbots: Algorithmic Aspects of Manipulating Programmable Matter with Finite Automata. https://arxiv.org/abs/1810.06360

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