CADbots: Algorithmic Aspects of Manipulating Programmable Matter with Finite Automata

Author:

Fekete Sándor P.ORCID,Gmyr Robert,Hugo Sabrina,Keldenich Phillip,Scheffer Christian,Schmidt Arne

Abstract

AbstractWe 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.

Funder

Deutsche Forschungsgemeinschaft

Projekt DEAL

Technische Universität Braunschweig

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computer Science Applications,General Computer Science

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