Two Computational Primitives for Algorithmic Self-Assembly:  Copying and Counting

Barish, Robert D.; Rothemund, Paul W. K.; Winfree, Erik

doi:10.1021/nl052038l

Cited by 203 publications

(182 citation statements)

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“…9 In principle, arbitrarily complex objects can be constructed using algorithmic self-assembly, 10 and objects including large finite-sized shapes and some circuit diagrams can be assembled from a small number of components. [11][12][13][14] Aperiodic one- 15,16 and two-dimensional 17,18 structures have been algorithmically self-assembled from programmable crystal monomers constructed from DNA tiles.…”

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confidence: 99%

Reducing Facet Nucleation during Algorithmic Self-Assembly

et al. 2007

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Algorithmic self-assembly, a generalization of crystal growth, has been proposed as a mechanism for bottom-up fabrication of complex nanostructures and autonomous DNA computation. In principle, growth can be programmed by designing a set of molecular tiles with binding interactions that enforce assembly rules. In practice, however, errors during assembly cause undesired products, drastically reducing yields. Here we provide experimental evidence that assembly can be made more robust to errors by adding redundant tiles that "proofread" assembly. We construct DNA tile sets for two methods, uniform and snaked proofreading. While both tile sets are predicted to reduce errors during growth, the snaked proofreading tile set is also designed to reduce nucleation errors on crystal facets. Using atomic force microscopy to image growth of proofreading tiles on ribbon-like crystals presenting long facets, we show that under the physical conditions we studied the rate of facet nucleation is 4-fold smaller for snaked proofreading tile sets than for uniform proofreading tile sets.

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Reducing Facet Nucleation during Algorithmic Self-Assembly

et al. 2007

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“…Since Winfree [19] first constructed the simple two-dimensional tiles using DNA strands to demonstrate the feasibility of computing through the self-assembling of tiles, Mao [10] came up with more complicated tiles (TX) to experimentally execute four steps of logical (cumulative XOR) operations. Barish et al [2] proposed and experimentally demonstrated an algorithmic self-assembly to perform two primitive computations: copying and counting. Fujibayashi et al [8] used tiles and DNA origami to grow crystals containing a cellular automaton pattern and proved that programmable molecular self-assembly may be sufficient to create a wide range of complex objects in one-pot reactions.…”

Section: Introductionmentioning

confidence: 99%

Parallel Solution to the Dominating Set Problem by Tile Assembly System

Zheng¹,

Huang²,

Xiao³

et al. 2014

Appl. Math. Inf. Sci.

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Abstract:The dominating set problem is a well known NP hard problem. It means that as the instance size grows, they quickly become impossible to solve on traditional digital computers. Tile assembly model has been demonstrated as a highly distributed parallel model of computation. Algorithmic tile assembly has been proved to be Turing-universal. This paper proposes a tile assembly system for the dominating set problem. It only needs Θ (mn) tile types to solve such a complex problem in the time Θ (m + n) where n and m are the number of vertices and edges of the given graph, respectively.

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“…Therefore, a parallel implementation of S SS , such as a DNA implementation like those in [12,13], with 2 n seeds has at least a 1 − 1 e ≥ 0.5 chance of correctly deciding whether a B, v ∈ SubsetSum. An implementation with 100 times as many seeds has at least a 1 − 1 e 100 chance.…”

Section: Where T Is Defined Bymentioning

confidence: 99%

“…While DNA computation suffers from relatively high error rates, the study of self-assembly shows how to utilize redundancy to design systems with built-in error correction [7,8,9,10,11]. Researchers have used DNA to assemble crystals with patterns of binary counters [12] and Sierpinski triangles [13], but while those crystals are deterministic, generating nondeterministic crystals may hold the power to solving complex problems quickly.…”

Section: Introductionmentioning

confidence: 99%

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Constant-Size Tileset for Solving an NP-Complete Problem in Nondeterministic Linear Time

Brun

DNA Computing

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Abstract. The tile assembly model, a formal model of crystal growth, is of special interest to computer scientists and mathematicians because it is universal [1]. Therefore, tile assembly model systems can compute all the functions that computers compute. In this paper, I formally define what it means for a system to nondeterministically decide a set, and present a system that solves an NP-complete problem called SubsetSum. Because of the nature of NP-complete problems, this system can be used to solve all NP problems in polynomial time, with high probability. While the proof that the tile assembly model is universal [2] implies the construction of such systems, those systems are in some sense "large" and "slow." The system presented here uses 49 = Θ(1) different tiles and computes in time linear in the input size. I also propose how such systems can be leveraged to program large distributed software systems.

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Two Computational Primitives for Algorithmic Self-Assembly: Copying and Counting

Cited by 203 publications

References 51 publications

Reducing Facet Nucleation during Algorithmic Self-Assembly

Reducing Facet Nucleation during Algorithmic Self-Assembly

Parallel Solution to the Dominating Set Problem by Tile Assembly System

Constant-Size Tileset for Solving an NP-Complete Problem in Nondeterministic Linear Time

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