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Signal Transmission Across Tile Assemblies: 3D Static Tiles Simulate Active Self-Assembly by 2D Signal-Passing Tiles | Jacob Hendricks
; Jennifer E. Padilla
; Matthew J. Patitz
; Trent A. Rogers
; | Date: |
20 Jun 2013 | Abstract: | The 2-Handed Assembly Model (2HAM) is a tile-based self-assembly model in
which, beginning from single tiles, arbitrarily large aggregations of static
tiles combine in pairs to form structures. The Signal-passing Tile Assembly
Model (STAM) is an extension of the 2HAM in which the tiles are dynamically
changing components which are able to alter their binding domains as they bind
together. In this paper, we prove that there exists a 3D tile set in the 2HAM
which is intrinsically universal for the class of all 2D STAM+ systems at
temperature 1 and 2 (where the STAM+ does not make use of the STAM’s power of
glue deactivation and assembly breaking, as the tile components of the 2HAM are
static and unable to change or break bonds). This means that there is a single
tile set U in the 3D 2HAM which can, for an arbitrarily complex STAM+ system S,
be configured with a single input configuration which causes U to exactly
simulate S at a scale factor dependent upon S. Furthermore, this simulation
uses only 2 planes of the third dimension. To achieve this result, we also
demonstrate useful techniques and transformations for converting an arbitrarily
complex STAM+ tile set into an STAM+ tile set where every tile has a constant,
low amount of complexity, in terms of the number and types of "signals" they
can send, with a trade off in scale factor. While the first result is of more
theoretical interest, showing the power of static tiles to simulate dynamic
tiles when given one extra plane in 3D, the second is of more practical
interest for the experimental implementation of STAM tiles, since it provides
potentially useful strategies for developing powerful STAM systems while
keeping the complexity of individual tiles low, thus making them easier to
physically implement. | Source: | arXiv, 1306.5005 | Services: | Forum | Review | PDF | Favorites |
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