Document Open Access Logo

Covert Computation in the Abstract Tile-Assembly Model

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



PDF
Thumbnail PDF

File

LIPIcs.SAND.2023.12.pdf
  • Filesize: 0.92 MB
  • 17 pages

Document Identifiers

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

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

Metrics

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

References

  1. Zachary Abel, Nadia Benbernou, Mirela Damian, Erik D. Demaine, Martin L. Demaine, Robin Flatland, Scott D. Kominers, and Robert Schweller. Shape replication through self-assembly and rnase enzymes. In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'10, pages 1045-1064, 2010. URL: https://doi.org/10.1137/1.9781611973075.85.
  2. Leonard M. Adleman, Qi Cheng, Ashish Goel, Ming-Deh A. Huang, David Kempe, Pablo Moisset de Espanés, and Paul W. K. Rothemund. Combinatorial optimization problems in self-assembly. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pages 23-32, 2002. Google Scholar
  3. Andrew Alseth and Matthew J. Patitz. The need for seed (in the abstract tile assembly model). In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SODA'23, pages 4540-4589, 2023. Google Scholar
  4. Spring Berman, Sándor P Fekete, Matthew J Patitz, and Christian Scheideler. Algorithmic foundations of programmable matter (dagstuhl seminar 18331). In Dagstuhl Reports, volume 8. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2019. Google Scholar
  5. Yuriy Brun. Arithmetic computation in the tile assembly model: Addition and multiplication. Theoretical Comp. Sci., 378:17-31, 2007. Google Scholar
  6. David Caballero, Timothy Gomez, Robert Schweller, and Tim Wylie. Covert computation in staged self-assembly: Verification is pspace-complete. In Proceedings of the 29th European Symposium on Algorithms, ESA'21, 2021. Google Scholar
  7. David Caballero, Timothy Gomez, Robert Schweller, and Tim Wylie. Verification and computation in restricted tile automata. Natural Computing, 2021. URL: https://doi.org/10.1007/s11047-021-09875-x.
  8. Angel A. Cantu, Austin Luchsinger, Robert Schweller, and Tim Wylie. Covert Computation in Self-Assembled Circuits. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), volume 132 of Leibniz International Proceedings in Informatics (LIPIcs), pages 31:1-31:14, 2019. Google Scholar
  9. Angel A. Cantu, Austin Luchsinger, Robert T. Schweller, and Tim Wylie. Covert computation in self-assembled circuits. Algorithmica, 83:531-552, 2019. Google Scholar
  10. Luis Ceze, Jeff Nivala, and Karin Strauss. Molecular digital data storage using dna. Nature Reviews Genetics, 20(8):456-466, 2019. Google Scholar
  11. Cameron Chalk, Austin Luchsinger, Robert Schweller, and Tim Wylie. Self-assembly of any shape with constant tile types using high temperature. In Proc. of the 26th Annual European Symposium on Algorithms, ESA'18, 2018. Google Scholar
  12. Cameron T. Chalk, Eric Martinez, Robert T. Schweller, Luis Vega, Andrew Winslow, and Tim Wylie. Optimal staged self-assembly of general shapes. Algorithmica, 80(4):1383-1409, 2018. URL: https://doi.org/10.1007/s00453-017-0318-0.
  13. Qi Cheng, Gagan Aggarwal, Michael H. Goldwasser, Ming-Yang Kao, Robert T. Schweller, and Pablo Moisset de Espanés. Complexities for generalized models of self-assembly. SIAM Journal on Computing, 34:1493-1515, 2005. Google Scholar
  14. Supreme Court. Ass'n for molecular pathology v. myriad, 2013. Google Scholar
  15. Erik Demaine, Matthew Patitz, Robert Schweller, and Scott Summers. Self-assembly of arbitrary shapes using rnase enzymes: Meeting the kolmogorov bound with small scale factor. Symposium on Theoretical Aspects of Computer Science (STACS2011), 9, January 2010. URL: https://doi.org/10.4230/LIPIcs.STACS.2011.201.
  16. Erik D. Demaine, Sándor P. Fekete, Christian Scheffer, and Arne Schmidt. New geometric algorithms for fully connected staged self-assembly. Theoretical Computer Science, 671:4-18, 2017. Computational Self-Assembly. URL: https://doi.org/10.1016/j.tcs.2016.11.020.
  17. David Doty, Lila Kari, and Benoît Masson. Negative interactions in irreversible self-assembly. Algorithmica, 66(1):153-172, 2013. Google Scholar
  18. David Doty, Jack H Lutz, Matthew J Patitz, Robert T Schweller, Scott M Summers, and Damien Woods. The tile assembly model is intrinsically universal. In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, pages 302-310. IEEE, 2012. Google Scholar
  19. Pim WJM Frederix, Ilias Patmanidis, and Siewert J Marrink. Molecular simulations of self-assembling bio-inspired supramolecular systems and their connection to experiments. Chemical Society Reviews, 47(10):3470-3489, 2018. Google Scholar
  20. David Furcy, Samuel Micka, and Scott M. Summers. Optimal program-size complexity for self-assembled squares at temperature 1 in 3d. Algorithmica, 77(4):1240-1282, March 2016. URL: https://doi.org/10.1007/s00453-016-0147-6.
  21. David Furcy, Scott M. Summers, and Logan Withers. Improved Lower and Upper Bounds on the Tile Complexity of Uniquely Self-Assembling a Thin Rectangle Non-Cooperatively in 3D. In Matthew R. Lakin and Petr Šulc, editors, 27th International Conference on DNA Computing and Molecular Programming (DNA 27), volume 205 of Leibniz International Proceedings in Informatics (LIPIcs), pages 4:1-4:18, Dagstuhl, Germany, 2021. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DNA.27.4.
  22. Daniel Hader, Aaron Koch, Matthew J Patitz, and Michael Sharp. The impacts of dimensionality, diffusion, and directedness on intrinsic universality in the abstract tile assembly model. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2607-2624. SIAM, 2020. Google Scholar
  23. Adam M Kabza, Nandini Kundu, Wenrui Zhong, and Jonathan T Sczepanski. Integration of chemically modified nucleotides with dna strand displacement reactions for applications in living systems. Wiley Interdisciplinary Reviews: Nanomedicine and Nanobiotechnology, 14(2):e1743, 2022. Google Scholar
  24. Alexandra Keenan, Robert Schweller, Michael Sherman, and Xingsi Zhong. Fast arithmetic in algorithmic self-assembly. Natural Computing, 15(1):115-128, March 2016. Google Scholar
  25. Paul WK Rothemund and Erik Winfree. The program-size complexity of self-assembled squares. In Proceedings of the thirty-second annual ACM symposium on Theory of computing, pages 459-468, 2000. Google Scholar
  26. Robert Schweller, Andrew Winslow, and Tim Wylie. Complexities for high-temperature two-handed tile self-assembly. In Robert Brijder and Lulu Qian, editors, DNA Computing and Molecular Programming, pages 98-109, Cham, 2017. Springer International Publishing. Google Scholar
  27. Heribert Vollmer. Introduction to Circuit Complexity. Springer Berlin Heidelberg, 1999. URL: https://doi.org/10.1007/978-3-662-03927-4.
  28. Klaus F Wagenbauer, Christian Sigl, and Hendrik Dietz. Gigadalton-scale shape-programmable dna assemblies. Nature, 552(7683):78-83, 2017. Google Scholar
  29. Erik Winfree. Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology, June 1998. Google Scholar
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