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Covert Computation in the Abstract Tile-Assembly Model

Authors Robert M. Alaniz, David Caballero, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, Tim Wylie

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Author Details

Robert M. Alaniz
  • Department of Computer Science, University of Texas Rio Grande Valley, TX, USA
David Caballero
  • Department of Computer Science, University of Texas Rio Grande Valley, TX, USA
Timothy Gomez
  • Department of Electrical Engineering and, Computer Science, Massachusetts Institute of, Technology, Cambridge, MA, USA
Elise Grizzell
  • Department of Computer Science, University of Texas Rio Grande Valley, TX, USA
Andrew Rodriguez
  • Department of Computer Science, University of Texas Rio Grande Valley, TX, USA
Robert Schweller
  • Department of Computer Science, University of Texas Rio Grande Valley, TX, USA
Tim Wylie
  • Department of Computer Science, University of Texas Rio Grande Valley, TX, USA

Funding

This research was supported in part by National Science Foundation Grant CCF-1817602.

Cite AsGet BibTex

Robert M. Alaniz, David Caballero, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Covert Computation in the Abstract Tile-Assembly Model. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SAND.2023.12

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • self-assembly
  • covert computation
  • atam

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