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The 3d Abstract Tile Assembly Model Is Intrinsically Universal, Aaron Koch, Daniel Hader, Matthew J. Patitz
The 3d Abstract Tile Assembly Model Is Intrinsically Universal, Aaron Koch, Daniel Hader, Matthew J. Patitz
Computer Science and Computer Engineering Undergraduate Honors Theses
In this paper, we prove that the three-dimensional abstract Tile Assembly Model (3DaTAM) is intrinsically universal. This means that there is a universal tile set in the 3DaTAM which can be used to simulate any 3DaTAM system. This result adds to a body of work on the intrinsic universality of models of self-assembly, and is specifically motivated by a result in FOCS 2016 showing that any intrinsically universal tile set for the 2DaTAM requires nondeterminism (i.e. undirectedness) even when simulating directed systems. To prove our result we have not only designed, but also fully implemented what we believe to be …