Kostitsyna, Irina, Wood, Cai and Woods, Damien (2024) Turning machines: a simple algorithmic model for molecular robotics. Natural Computing, 23 (2). pp. 407-430. ISSN 1572-9796
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Abstract
Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We provide a suite of tools for reasoning about Turning Machines by fully characterising their ability to execute line rotations: executing an almost-full line rotation of $$5\pi /3$$ 5 π / 3 radians is possible, yet a full $$2\pi$$ 2 π rotation is impossible. Furthermore, line rotations up to $$5\pi /3$$ 5 π / 3 are executed efficiently, in $$O(\log n)$$ O ( log n ) expected time in our continuous time Markov chain time model. We then show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold shapes. In particular, arbitrarily large zig-zag-rastered squares and zig-zag paths are foldable, as are y -monotone shapes albeit with error (bounded by perimeter length). Finally, we give shapes that despite having paths that traverse all their points, are in fact impossible to fold, as well as techniques for folding certain classes of (scaled) shapes without error. Our approach relies on careful geometric-based analyses of the feats possible and impossible by a very simple robotic system, and pushes conceptional hardness towards mathematical analysis and away from molecular implementation.
Item Type: | Article |
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Keywords: | Model of computation; Algorithmic molecular robotics; Self-assembly; Nubot; Reconfiguration; |
Academic Unit: | Faculty of Science and Engineering > Computer Science |
Item ID: | 19694 |
Identification Number: | 10.1007/s11047-022-09880-8 |
Depositing User: | Damien Woods |
Date Deposited: | 14 Apr 2025 14:51 |
Journal or Publication Title: | Natural Computing |
Publisher: | Springer |
Refereed: | Yes |
Related URLs: | |
URI: | https://mural.maynoothuniversity.ie/id/eprint/19694 |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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