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    The Tile Assembly Model is Intrinsically Universal


    Doty, David and Lutz, Jack H. and Patitz, Matthew J. and Schweller, Robert T. and Summers, Scott M. and Woods, Damien (2012) The Tile Assembly Model is Intrinsically Universal. 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science. pp. 302-310. ISSN 0272-5428

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    Abstract

    We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T. The simulation is "intrinsic" in the sense that the self-assembly process carried out by U is exactly that carried out by T, with each tile of T represented by an m × m "super tile" of U. Our construction works for the full aTAM at any temperature, and it faithfully simulates the deterministic or nondeterministic behavior of each T. Our construction succeeds by solving an analog of the cell differentiation problem in developmental biology: Each super tile of U, starting with those in the seed assembly, carries the "genome" of the simulated system T. At each location of a potential super tile in the self-assembly of U, a decision is made whether and how to express this genome, i.e., whether to generate a super tile and, if so, which tile of T it will represent. This decision must be achieved using asynchronous communication under incomplete information, but it achieves the correct global outcome(s).

    Item Type: Article
    Keywords: tile; assembly; model; intrinsically; universal;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 15724
    Identification Number: https://doi.org/10.1109/FOCS.2012.76
    Depositing User: Damien Woods
    Date Deposited: 22 Mar 2022 16:41
    Journal or Publication Title: 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
    Publisher: IEEE
    Refereed: Yes
    URI:

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