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DOI: 10.4230/LIPIcs.ISAAC.2022.37
On Algorithmic Self-Assembly of Squares by Co-Transcriptional Folding

Authors: Szilárd Zsolt Fazekas, Hwee Kim, Ryuichi Matsuoka, Shinnosuke Seki, and Hinano Takeuchi

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
Algorithms play a primary role in programming an orchestrated self-assembly of shapes into molecules. In this paper, we study the algorithmic self-assembly of squares by RNA co-transcriptional folding in its oritatami model. We formalize the square self-assembly problem in oritatami and propose a universal oritatami transcript made of 939 types of abstract molecules (beads) and of period 1294 that folds deterministically and co-transcriptionally at delay 3 and maximum arity into the n × n square modulo horizontal and vertical scaling factors for all sufficiently large n’s after building a Θ(log n) width "ruler" that measures n upon the seed of size Θ(log n) on which n is encoded in binary.
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Szilárd Zsolt Fazekas, Hwee Kim, Ryuichi Matsuoka, Shinnosuke Seki, and Hinano Takeuchi. On Algorithmic Self-Assembly of Squares by Co-Transcriptional Folding. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fazekas_et_al:LIPIcs.ISAAC.2022.37,
  author =	{Fazekas, Szil\'{a}rd Zsolt and Kim, Hwee and Matsuoka, Ryuichi and Seki, Shinnosuke and Takeuchi, Hinano},
  title =	{{On Algorithmic Self-Assembly of Squares by Co-Transcriptional Folding}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.37},
  URN =		{urn:nbn:de:0030-drops-173228},
  doi =		{10.4230/LIPIcs.ISAAC.2022.37},
  annote =	{Keywords: Algorithmic molecular self-assembly, Co-transcriptional folding, Oritatami system, Self-assembly of squares}
}
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