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    Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time

    Woods, Damien and Chen, Ho-Lin and Goodfriend, Scott and Dabby, Nadine and Winfree, Erik and Yin, Peng (2013) Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time. ITCS: Proceedings of the 4th conference on Innovations in Theoretical Computer Science. pp. 353-354.

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    We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by biology's fantastic ability to assemble biomolecules that form systems with complicated structure and dynamics, from molecular motors that walk on rigid tracks and proteins that dynamically alter the structure of the cell during mitosis, to embryonic development where large-scale complicated organisms efficiently grow from a single cell. Using this active self-assembly model, we show how to efficiently self-assemble shapes and patterns from simple monomers. For example, we show how to grow a line of monomers in time and number of monomer states that is merely logarithmic in the length of the line. Our main results show how to grow arbitrary connected two-dimensional geometric shapes and patterns in expected time that is polylogarithmic in the size of the shape, plus roughly the time required to run a Turing machine deciding whether or not a given pixel is in the shape. We do this while keeping the number of monomer types logarithmic in shape size, plus those monomers required by the Kolmogorov complexity of the shape or pattern. This work thus highlights the efficiency advantages of active self-assembly over passive self-assembly and motivates experimental effort to construct general-purpose active molecular self-assembly systems.

    Item Type: Article
    Keywords: Self-assembly; model of computation; molecular programming; reconfigurable robotics;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 15721
    Depositing User: Damien Woods
    Date Deposited: 22 Mar 2022 16:18
    Journal or Publication Title: ITCS: Proceedings of the 4th conference on Innovations in Theoretical Computer Science
    Publisher: ACM Digital Library
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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