Joint with Sudheer Sahu & John Reif
In Proc. Tenth International Meeting on DNA Computing, 2004
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Abstract: The self-assembly process for bottom-up
construction of nanostructures is of key importance to the emerging scientific
discipline Nanoscience. However, self-assembly at the molecular scale is prone
to a quite high rate of error. Such high error rate is a major barrier to
large-scale experimental implementation of DNA tiling. The goals of this paper
are to develop theoretical methods for compact error-resilient self-assembly
and to analyze these methods by thermodynamic analysis and computer simulation.
Prior work by Winfree provided an innovative approach to decrease tiling self-assembly
errors without decreasing the intrinsic error rate $\epsilon$ of assembling
a single tile. However, his technique resulted in a final structure that
is larger than the original one (four times larger for decreasing the error
to $\epsilon^2$, nine times for to $\epsilon^3$). In this chapter, we describe
various compact error-resilient tiling methods that do not increase
the size of the tiling assembly. These methods apply to the assembly of Boolean
arrays which perform input sensitive computations (among other computations).
Our 2-way (3-way) overlay redundancy construction decreases the error rate
from $\epsilon$ to approximately $\epsilon^2$ ($\epsilon^3$), without increasing
the size of the assembly. As in Winfree's constructions, the number of distinct
tile types required is also increased in our error-resilient tiling constructions.
These results were further validated using computer simulation.
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