Turning machines

Irina Kostitsyna, Cai Wood, Damien Woods

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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 fully characterise the ability of Turning Machines to execute line rotations, and to do so efficiently: computing an almost-full line rotation of 5π/3 radians is possible, yet a full 2π rotation is impossible. We show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold arbitrarily large zig-zag-rastered squares and y-monotone shapes.

Original languageEnglish
Title of host publication26th International Conference on DNA Computing and Molecular Programming, DNA 2020
EditorsCody Gear, Matthew J. Patitz
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
ISBN (Electronic)9783959771634
DOIs
Publication statusPublished - 1 Sep 2020
Event26th International Conference on DNA Computing and Molecular Programming, DNA 2020 - Oxford, United Kingdom
Duration: 14 Sep 202017 Sep 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume174
ISSN (Print)1868-8969

Conference

Conference26th International Conference on DNA Computing and Molecular Programming, DNA 2020
CountryUnited Kingdom
CityOxford
Period14/09/2017/09/20

Keywords

  • Model of computation
  • Molecular robotics
  • Nubot
  • Reconfiguration
  • Self-assembly

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