1 research outputs found
Geometric Tiles and Powers and Limitations of Geometric Hindrance in Self-Assembly
Tile-based self-assembly systems are capable of universal computation and
algorithmically-directed growth. Systems capable of such behavior typically
make use of "glue cooperation" in which the glues on at least sides of a
tile must match and bind to those exposed on the perimeter of an assembly for
that tile to attach. However, several models have been developed which utilize
"weak cooperation", where only a single glue needs to bind but other
preventative forces (such as geometric, or steric, hindrance) provide
additional selection for which tiles may attach, and where this allows for
algorithmic behavior. In this paper we first work in a model where tiles are
allowed to have geometric bumps and dents on their edges. We show how such
tiles can simulate systems of square tiles with complex glue functions (using
asymptotically optimal sizes of bumps and dents), and also how they can
simulate weakly cooperative systems in a model which allows for duples (i.e.
tiles either twice as long or twice as tall as square tiles). We then show that
with only weak cooperation via geometric hindrance, no system in any model can
simulate even a class of tightly constrained, deterministic cooperative
systems, further defining the boundary of what is possible using this tool.Comment: Extended version of the 14-page paper to appear in the proceedings of
UCNC 201