Document Open Access Logo

Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly

Authors Tim Gomez, Elise Grizzell , Asher Haun , Ryan Knobel, Tom Peters , Robert Schweller, Tim Wylie

PDF

File

Thumbnail PDF
PDF
LIPIcs.SAND.2025.24.pdf
  • Filesize: 0.65 MB
  • 6 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Intrinsic Universality
  • Tile Automata
  • Cellular Automata
  • Self-assembly

Metrics

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

Abstract

The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system Γ, (b) the dynamics involved in building Γ’s assemblies, and (c) Γ’s internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile’s potential attachment or transition by selecting its state in a single step, considering all possible outcomes until the moment of selection.
The system uses supertiles, each encoding the complete system being simulated. The universal system builds supertiles from its seed, each representing a single tile in Γ, transferring the information to simulate Γ to each new tile. Supertiles may also asynchronously transition states according to the rules of Γ. This result also implies IU for pairwise asynchronous Cellular Automata.

Cite As Get BibTex

Tim Gomez, Elise Grizzell, Asher Haun, Ryan Knobel, Tom Peters, Robert Schweller, and Tim Wylie. Brief Announcement: Intrinsic Universality in Seeded Active Tile Self-Assembly. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 24:1-24:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.24

Author Details

Tim Gomez
  • CSAIL, MIT, Cambridge, MA, USA
Elise Grizzell
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Asher Haun
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Ryan Knobel
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Tom Peters
  • TU Eindhoven, The Netherlands
Robert Schweller
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Tim Wylie
  • University of Texas Rio Grande Valley, Edinburg, TX, USA

Funding

This research was supported in part by National Science Foundation Grant CCF-2329918.

References

  1. Edwin Roger Banks. Universality in cellular automata. In 11th Annual Symposium on Switching and Automata Theory (swat), pages 194-215, 1970. URL: https://doi.org/10.1109/SWAT.1970.27.
  2. Cameron Chalk, Austin Luchsinger, Eric Martinez, Robert Schweller, Andrew Winslow, and Tim Wylie. Freezing Simulates Non-freezing Tile Automata. In DNA Computing and Molecular Programming, pages 155-172, 2018. URL: https://doi.org/10.1007/978-3-030-00030-1.
  3. Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Matthew J. Patitz, Robert T. Schweller, Andrew Winslow, and Damien Woods. One Tile to Rule Them All: Simulating Any Turing Machine, Tile Assembly System, or Tiling System with a Single Puzzle Piece. ArXiv e-Prints, 2012. URL: https://doi.org/10.48550/arXiv.1212.4756.
  4. 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 53rd Annual Symposium on Foundations of Computer Science, pages 302-310, 2012. URL: https://doi.org/10.1109/FOCS.2012.76.
  5. David Doty, Jack H Lutz, Matthew J Patitz, Scott M Summers, and Damien Woods. Intrinsic Universality in Self-Assembly. In 27th International Symposium on Theoretical Aspects of Computer Science (2010), 2010. URL: https://doi.org/10.4230/LIPIcs.STACS.2010.2461.
  6. Bruno Durand and Zsuzsanna Róka. The game of life: universality revisited. In Cellular Automata: a Parallel Model, pages 51-74, 1999. URL: https://doi.org/10.1007/978-94-015-9153-9_2.
  7. Tim Gomez, Elise Grizzell, Asher Haun, Ryan Knobel, Tom Peters, Robert Schweller, and Tim Wylie. Intrinsic universality in seeded active tile self-assembly, 2024. URL: https://arxiv.org/abs/2407.11545.
  8. 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 Symposium on Discrete Algorithms (SODA), pages 2607-2624, 2019. Google Scholar
  9. Pierre-Étienne Meunier, Matthew J. Patitz, Scott M. Summers, Guillaume Theyssier, Andrew Winslow, and Damien Woods. Intrinsic universality in tile self-assembly requires cooperation. In 25th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 752-771, 2014. URL: https://doi.org/10.1137/1.9781611973402.56.
  10. J. von Neumann. Theory of self-reproducing automata. Urbana, U. of Illinois Press, 1966. Google Scholar
  11. Erik Winfree. Algorithmic self-assembly of DNA. California Institute of Technology, 1998. Google Scholar
  12. Thomas Worsch. Towards intrinsically universal asynchronous CA. Natural Computing, 12:539-550, 2013. URL: https://doi.org/10.1007/s11047-013-9388-3.
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
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact