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Small Tile Sets That Compute While Solving Mazes

Authors: Matthew Cook, Tristan Stérin, and Damien Woods

Published in: LIPIcs, Volume 205, 27th International Conference on DNA Computing and Molecular Programming (DNA 27) (2021)

Abstract

We ask the question of how small a self-assembling set of tiles can be yet have interesting computational behaviour. We study this question in a model where supporting walls are provided as an input structure for tiles to grow along: we call it the Maze-Walking Tile Assembly Model. The model has a number of implementation prospects, one being DNA strands that attach to a DNA origami substrate. Intuitively, the model suggests a separation of signal routing and computation: the input structure (maze) supplies a routing diagram, and the programmer’s tile set provides the computational ability. We ask how simple the computational part can be. We give two tiny tile sets that are computationally universal in the Maze-Walking Tile Assembly Model. The first has four tiles and simulates Boolean circuits by directly implementing NAND, NXOR and NOT gates. Our second tile set has 6 tiles and is called the Collatz tile set as it produces patterns found in binary/ternary representations of iterations of the Collatz function. Using computer search we find that the Collatz tile set is expressive enough to encode Boolean circuits using blocks of these patterns. These two tile sets give two different methods to find simple universal tile sets, and provide motivation for using pre-assembled maze structures as circuit wiring diagrams in molecular self-assembly based computing.

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Matthew Cook, Tristan Stérin, and Damien Woods. Small Tile Sets That Compute While Solving Mazes. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cook_et_al:LIPIcs.DNA.27.8,
  author =	{Cook, Matthew and St\'{e}rin, Tristan and Woods, Damien},
  title =	{{Small Tile Sets That Compute While Solving Mazes}},
  booktitle =	{27th International Conference on DNA Computing and Molecular Programming (DNA 27)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-205-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{205},
  editor =	{Lakin, Matthew R. and \v{S}ulc, Petr},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.27.8},
  URN =		{urn:nbn:de:0030-drops-146758},
  doi =		{10.4230/LIPIcs.DNA.27.8},
  annote =	{Keywords: model of computation, self-assembly, small universal tile set, Boolean circuits, maze-solving}
}

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DOI: 10.4230/LIPIcs.DNA.2020.9

scadnano: A Browser-Based, Scriptable Tool for Designing DNA Nanostructures

Authors: David Doty, Benjamin L Lee, and Tristan Stérin

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

We introduce scadnano (short for "scriptable cadnano"), a computational tool for designing synthetic DNA structures. Its design is based heavily on cadnano [Douglas et al., 2009], the most widely-used software for designing DNA origami [Paul W. K. Rothemund, 2006], with three main differences: 1) scadnano runs entirely in the browser, with no software installation required. 2) scadnano designs, while they can be edited manually, can also be created and edited by a well-documented Python scripting library, to help automate tedious tasks. 3) The scadnano file format is easily human-readable. This goal is closely aligned with the scripting library, intended to be helpful when debugging scripts or interfacing with other software. The format is also somewhat more expressive than that of cadnano, able to describe a broader range of DNA structures than just DNA origami.

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David Doty, Benjamin L Lee, and Tristan Stérin. scadnano: A Browser-Based, Scriptable Tool for Designing DNA Nanostructures. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{doty_et_al:LIPIcs.DNA.2020.9,
  author =	{Doty, David and Lee, Benjamin L and St\'{e}rin, Tristan},
  title =	{{scadnano: A Browser-Based, Scriptable Tool for Designing DNA Nanostructures}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.9},
  URN =		{urn:nbn:de:0030-drops-129624},
  doi =		{10.4230/LIPIcs.DNA.2020.9},
  annote =	{Keywords: computer-aided design, structural DNA nanotechnology, DNA origami}
}

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Documents authored by Stérin, Tristan

Small Tile Sets That Compute While Solving Mazes

Abstract

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scadnano: A Browser-Based, Scriptable Tool for Designing DNA Nanostructures

Abstract

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