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.
CITATION STYLE
Fekete, S. P., Gmyr, R., Hugo, S., Keldenich, P., Scheffer, C., & Schmidt, A. (2020). CADbots: Algorithmic Aspects of Manipulating Programmable Matter with Finite Automata. In Springer Proceedings in Advanced Robotics (Vol. 14, pp. 727–743). Springer Science and Business Media B.V. https://doi.org/10.1007/978-3-030-44051-0_42
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