Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact Error-Resilient Self-Assembly of Recursively Defined Patterns   A limitation to molecular implementations of tile-based self-assembly systems
is the high rate of mismatch errors which has been observed to be between 1%
and 10%. Controlling the physical conditions of the system to reduce this
intrinsic error rate $\epsilon$ prohibitively slows the growth rate of the
system. This has motivated the development of techniques to redundantly encode
information in the tiles of a system in such a way that the rate of mismatch
errors in the final assembly is reduced even without a reduction in $\epsilon$.
Winfree and Bekbolatov, and Chen and Goel, introduced such error-resilient
systems that reduce the mismatch error rate to $\epsilon^k$ by replacing each
tile in an error-prone system with a $k \times k$ block of tiles in the
error-resilient system, but this increases the number of tile types used by a
factor of $k^2$, and the scale of the pattern produced by a factor of $k$.
Reif, Sahu and Yin, and Sahu and Reif, introduced compact error-resilient
systems for the self-assembly of Boolean arrays that reduce the mismatch error
rate to $\epsilon^2$ without increasing the scale of the pattern produced. In
this paper, we give a technique to design compact error-resilient systems for
the self-assembly of the recursively defined patterns introduced by Kautz and
Lathrop. We show that our compact error-resilient systems reduce the mismatch
error rate to $\epsilon^2$ by using the independent error model introduced by
Sahu and Reif. Surprisingly, our error-resilient systems use the same number of
tile types as the error-prone system from which they are constructed.

27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con