License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SAND.2023.12
URN: urn:nbn:de:0030-drops-179482
URL: https://drops.dagstuhl.de/opus/volltexte/2023/17948/
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Alaniz, Robert M. ; Caballero, David ; Gomez, Timothy ; Grizzell, Elise ; Rodriguez, Andrew ; Schweller, Robert ; Wylie, Tim

Covert Computation in the Abstract Tile-Assembly Model

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LIPIcs-SAND-2023-12.pdf (0.9 MB)


Abstract

There have been many advances in molecular computation that offer benefits such as targeted drug delivery, nanoscale mapping, and improved classification of nanoscale organisms. This power led to recent work exploring privacy in the computation, specifically, covert computation in self-assembling circuits. Here, we prove several important results related to the concept of a hidden computation in the most well-known model of self-assembly, the Abstract Tile-Assembly Model (aTAM). We show that in 2D, surprisingly, the model is capable of covert computation, but only with an exponential-sized assembly. We also show that the model is capable of covert computation with polynomial-sized assemblies with only one step in the third dimension (just-barely 3D). Finally, we investigate types of functions that can be covertly computed as members of P/Poly.

BibTeX - Entry

@InProceedings{alaniz_et_al:LIPIcs.SAND.2023.12,
  author =	{Alaniz, Robert M. and Caballero, David and Gomez, Timothy and Grizzell, Elise and Rodriguez, Andrew and Schweller, Robert and Wylie, Tim},
  title =	{{Covert Computation in the Abstract Tile-Assembly Model}},
  booktitle =	{2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-275-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{257},
  editor =	{Doty, David and Spirakis, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17948},
  URN =		{urn:nbn:de:0030-drops-179482},
  doi =		{10.4230/LIPIcs.SAND.2023.12},
  annote =	{Keywords: self-assembly, covert computation, atam}
}

Keywords: self-assembly, covert computation, atam
Collection: 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023)
Issue Date: 2023
Date of publication: 12.06.2023


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