27,389 research outputs found
DNA-BASED SELF-ASSEMBLY AND NANOROBOTICS: THEORY AND EXPERIMENTS
We study the following fundamental questions in DNA-based self-assembly and nanorobotics: How to control errors in self-assembly? How to construct complex nanoscale objects in simpler ways? How to transport nanoscale objects in programmable manner? Fault tolerance in self-assembly: Fault tolerant self-assembly is important for nanofab-rication and nanocomputing applications. It is desirable to design compact error-resilient schemes that do not result in the increase in the original size of the assemblies. We present a comprehensive theory of compact error-resilient schemes for algorithmic self-assembly in two and three dimensions, and discuss the limitations and capabilities of redundancy based compact error correction schemes. New and powerful self-assembly model: We develop a reversible self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. Under our time-dependent glue model, we can rigorously study and demonstrate catalysis and self-replication in the tile assembly. We can assemble thin rectangles of size k × N using O
Size-Dependent Tile Self-Assembly: Constant-Height Rectangles and Stability
We introduce a new model of algorithmic tile self-assembly called
size-dependent assembly. In previous models, supertiles are stable when the
total strength of the bonds between any two halves exceeds some constant
temperature. In this model, this constant temperature requirement is replaced
by an nondecreasing temperature function that depends on the size of the smaller of the two halves. This
generalization allows supertiles to become unstable and break apart, and
captures the increased forces that large structures may place on the bonds
holding them together.
We demonstrate the power of this model in two ways. First, we give fixed tile
sets that assemble constant-height rectangles and squares of arbitrary input
size given an appropriate temperature function. Second, we prove that deciding
whether a supertile is stable is coNP-complete. Both results contrast with
known results for fixed temperature.Comment: In proceedings of ISAAC 201
Optimal Staged Self-Assembly of General Shapes
We analyze the number of tile types , bins , and stages necessary to
assemble squares and scaled shapes in the staged tile assembly
model. For squares, we prove stages suffice and
are necessary for almost all .
For shapes with Kolmogorov complexity , we prove
stages suffice and are necessary to
assemble a scaled version of , for almost all . We obtain similarly tight
bounds when the more powerful flexible glues are permitted.Comment: Abstract version appeared in ESA 201
Signal Transmission Across Tile Assemblies: 3D Static Tiles Simulate Active Self-Assembly by 2D Signal-Passing Tiles
The 2-Handed Assembly Model (2HAM) is a tile-based self-assembly model in
which, typically 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. For our first result, we 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.
Using these simplifications, we prove that for each temperature
there exists a 3D tile set in the 2HAM which is intrinsically universal for the
class of all 2D STAM systems at temperature (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 in the 3D 2HAM which
can, for an arbitrarily complex STAM system , be configured with a
single input configuration which causes to exactly simulate at a scale
factor dependent upon . Furthermore, this simulation uses only two planes of
the third dimension. This implies that there exists a 3D tile set at
temperature in the 2HAM which is intrinsically universal for the class of
all 2D STAM systems at temperature . Moreover, we show that for each
temperature there exists an STAM tile set which is intrinsically
universal for the class of all 2D STAM systems at temperature ,
including the case where .Comment: A condensed version of this paper will appear in a special issue of
Natural Computing for papers from DNA 19. This full version contains proofs
not seen in the published versio
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