Document Open Access Logo

Turning Machines

Authors Irina Kostitsyna, Cai Wood, Damien Woods

PDF
Thumbnail PDF

File

LIPIcs.DNA.2020.11.pdf
  • Filesize: 1.34 MB
  • 21 pages

Document Identifiers

Author Details

Irina Kostitsyna
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Cai Wood
  • Hamilton Institute and Department of Theoretical Physics, Maynooth University, Ireland
Damien Woods
  • Hamilton Institute and Department of Computer Science, Maynooth University, Ireland

Funding

Authors C. Wood and D. Woods are supported by European Research Council (ERC) award number 772766 and Science foundation Ireland (SFI) grant 18/ERCS/5746 (this manuscript reflects only the authors' view and the ERC is not responsible for any use that may be made of the information it contains).

Acknowledgements

We thank Vera Sacristán and Suneeta Ramaswami for insightful ideas and important input. This work began at the 29th Bellairs Winter Workshop on Computational Geometry (March 21-28, 2014 in Holetown, Barbados), we thank Erik Demaine for organising a wonderful workshop and providing valuable feedback, and the rest of the participants for providing a stimulating environment. We also thank Dave Doty and Nicolas Schabanel for helpful comments.

Cite As Get BibTex

Irina Kostitsyna, Cai Wood, and Damien Woods. Turning Machines. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.DNA.2020.11

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • model of computation
  • molecular robotics
  • self-assembly
  • nubot
  • reconfiguration

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D Demaine, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Suneeta Ramaswami, Vera Sacristán, and Stefanie Wuhrer. Linear reconfiguration of cube-style modular robots. Computational Geometry, 42(6-7):652-663, 2009. Google Scholar
  2. Greg Aloupis, Sébastien Collette, Erik D. Demaine, Stefan Langerman, Vera Sacristán, and Stefanie Wuhrer. Reconfiguration of cube-style modular robots using O(log n) parallel moves. In International Symposium on Algorithms and Computation, pages 342-353. Springer, 2008. Google Scholar
  3. Ho-Lin Chen, David Doty, Dhiraj Holden, Chris Thachuk, Damien Woods, and Chun-Tao Yang. Fast algorithmic self-assembly of simple shapes using random agitation. In DNA20: The 20th International Conference on DNA Computing and Molecular Programming, volume 8727 of LNCS, pages 20-36, Kyoto, Japan, September 2014. Springer. Full version: URL: http://arxiv.org/abs/1409.4828.
  4. Moya Chen, Doris Xin, and Damien Woods. Parallel computation using active self-assembly. Natural Computing, 14(2):225-250, 2014. arXiv version: URL: http://arxiv.org/abs/1405.0527.
  5. Kenneth C. Cheung, Erik D. Demaine, Jonathan R. Bachrach, and Saul Griffith. Programmable assembly with universally foldable strings (moteins). IEEE Transactions on Robotics, 27(4):718-729, 2011. Google Scholar
  6. Yen-Ru Chin, Jui-Ting Tsai, and Ho-Lin Chen. A minimal requirement for self-assembly of lines in polylogarithmic time. Natural Computing, 17(4):743-757, 2018. Google Scholar
  7. Robert Connelly, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Stefan Langerman, Joseph S.B. Mitchell, Ares Ribó, and Günter Rote. Locked and unlocked chains of planar shapes. Discrete & Computational Geometry, 44(2):439-462, 2010. Google Scholar
  8. Nadine Dabby and Ho-Lin Chen. Active self-assembly of simple units using an insertion primitive. In SODA: The 24th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1526-1536, January 2012. Google Scholar
  9. Rachel E. Dawes-Hoang, Kush M. Parmar, Audrey E. Christiansen, Chris B. Phelps, Andrea H. Brand, and Eric F. Wieschaus. Folded gastrulation, cell shape change and the control of myosin localization. Development, 132(18):4165-4178, 2005. Google Scholar
  10. Erik D. Demaine, Jacob Hendricks, Meagan Olsen, Matthew J. Patitz, Trent A. Rogers, Nicolas Schabanel, Shinnosuke Seki, and Hadley Thomas. Know when to fold'em: self-assembly of shapes by folding in oritatami. In DNA: International Conference on DNA Computing and Molecular Programming, pages 19-36. Springer, 2018. Google Scholar
  11. Cody Geary, Pierre-Étienne Meunier, Nicolas Schabanel, and Shinnosuke Seki. Programming biomolecules that fold greedily during transcription. In MFCS: The 41st International Symposium on Mathematical Foundations of Computer Science. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2016. Google Scholar
  12. Robert Gmyr, Kristian Hinnenthal, Irina Kostitsyna, Fabian Kuhn, Dorian Rudolph, Christian Scheideler, and Thim Strothmann. Forming tile shapes with simple robots. Natural Computing, pages 1-16, 2019. Google Scholar
  13. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete mathematics, 1989. Google Scholar
  14. Benjamin Hescott, Caleb Malchik, and Andrew Winslow. Tight bounds for active self-assembly using an insertion primitive. Algorithmica, 77:537-554, 2017. Google Scholar
  15. Benjamin Hescott, Caleb Malchik, and Andrew Winslow. Non-determinism reduces construction time in active self-assembly using an insertion primitive. In COCOON: The 24th International Computing and Combinatorics Conference, pages 626-637. Springer, 2018. Google Scholar
  16. Chun-Ying Hou and Ho-Lin Chen. An exponentially growing nubot system without state changes. In International Conference on Unconventional Computation and Natural Computation, pages 122-135. Springer, 2019. Google Scholar
  17. Adam C Martin, Matthias Kaschube, and Eric F Wieschaus. Pulsed contractions of an actin-myosin network drive apical constriction. Nature, 457(7228):495-499, 2008. Google Scholar
  18. Othon Michail, George Skretas, and Paul G. Spirakis. On the transformation capability of feasible mechanisms for programmable matter. Journal of Computer and System Sciences, 102:18-39, 2019. Google Scholar
  19. Hamid Ramezani and Hendrik Dietz. Building machines with DNA molecules. Nature Reviews Genetics, pages 1-22, 2019. Google Scholar
  20. Damien Woods, Ho-Lin Chen, Scott Goodfriend, Nadine Dabby, Erik Winfree, and Peng Yin. Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In ITCS: The 4th conference on Innovations in Theoretical Computer Science, pages 353-354. ACM, 2013. Full version: http://arxiv.org/abs/1301.2626 [cs.DS].
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact