562 research outputs found
Intrinsic universality and the computational power of self-assembly
This short survey of recent work in tile self-assembly discusses the use of
simulation to classify and separate the computational and expressive power of
self-assembly models. The journey begins with the result that there is a single
universal tile set that, with proper initialization and scaling, simulates any
tile assembly system. This universal tile set exhibits something stronger than
Turing universality: it captures the geometry and dynamics of any simulated
system. From there we find that there is no such tile set in the
noncooperative, or temperature 1, model, proving it weaker than the full tile
assembly model. In the two-handed or hierarchal model, where large assemblies
can bind together on one step, we encounter an infinite set, of infinite
hierarchies, each with strictly increasing simulation power. Towards the end of
our trip, we find one tile to rule them all: a single rotatable flipable
polygonal tile that can simulate any tile assembly system. It seems this could
be the beginning of a much longer journey, so directions for future work are
suggested.Comment: In Proceedings MCU 2013, arXiv:1309.104
Nascent nanocomputers: DNA self-assembly in O(1) stages
DNA self-assembly offers a potential for nanoscale microcircuits and computers. To make that potential possible requires the development of reliable and efficient tile assembly models. Efficiency is often achieved by minimizing tile complexity, as well as by evaluating the cost and reliability of the specific elements of each tile assembly model. We consider a 2D tile assembly model at temperature 1. The standard 2D tile assembly model at temperature 1 has a tile complexity of O(n) for the construction of exact, complete n x n squares. However, previous research found a staged tile assembly model achieved a tile complexity of O(1) to construct n x n squares, with O(logn) stages. Our staged tile assembly model achieves a tile complexity of O(logn) using only O(1) stages to construct n x n squares
Limitations of Self-Assembly at Temperature One (extended abstract)
We prove that if a subset X of the integer Cartesian plane weakly
self-assembles at temperature 1 in a deterministic (Winfree) tile assembly
system satisfying a natural condition known as *pumpability*, then X is a
finite union of doubly periodic sets. This shows that only the most simple of
infinite shapes and patterns can be constructed using pumpable temperature 1
tile assembly systems, and gives strong evidence for the thesis that
temperature 2 or higher is required to carry out general-purpose computation in
a tile assembly system. Finally, we show that general-purpose computation is
possible at temperature 1 if negative glue strengths are allowed in the tile
assembly model
- …