Arithmetic computation using self-assembly of DNA tiles: subtraction and division

Zhang, Xuncai; Wang, Yanfeng; Chen, Zhihua; Xu, Jin; Cui, Guangzhao

doi:10.1016/j.pnsc.2008.07.013

Cited by 19 publications

(33 citation statements)

References 22 publications

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“…further extended Brun's technique and presented the basic operations of binary subtraction and division based on the tile self‐assembly model. [ 98 ] At the same time, Fujibayashi et al. proposed an improved error suppression mechanism, adding a short additional DNA strand to each sticky end of the tile to further reduce the mismatch rate and yield a more reliable computing result.…”

Section: Synthetic Dna For Computingmentioning

confidence: 99%

Toward Smart Information Processing with Synthetic DNA Molecules

Chu

Zhang

Wang

et al. 2021

Macromol. Rapid Commun.

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DNA, a biological macromolecule, is a naturally evolved information material. From the structural point of view, an individual DNA strand can be considered as a chain of data with its bases working as single units. For decades, due to the high biochemical stability, large information storage capacity, and high recognition specificity, DNA has been recognized as an attractive material for information processing. Especially, the chemical synthesis strategies and DNA sequencing techniques have been rapidly developed recently, further enabling encoding information with synthetic DNA molecules. Herein, recent progresses are summarized on information processing based on synthetic DNA molecules from three aspects including information storage, computation, and encryption, and proposed the challenges and future development directions.

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Section: Synthetic Dna For Computingmentioning

confidence: 99%

Toward Smart Information Processing with Synthetic DNA Molecules

Chu

Zhang

Wang

et al. 2021

Macromol. Rapid Commun.

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“…also came up with computational tiles for subtraction and division of integers, again, using O 1 computational tiles. The running time complexity is O n for subtraction and O n 2 for division [1]. Additionally, open source softwares such as XTile (it can convert any computational tile formula to a .tile file supported XGrow [16]), ISU TAS [17] and XtileMod (it can generate required computational tiles for performing arithmetic operations as well as the corresponding .tiles file for DNA tiles) have been developed [18,19].…”

Section: Introductionmentioning

confidence: 99%

“…al. gave computational DNA tiles to perform division of a number but the output had integer quotient [1]. In this work, we simply modify their method of division to improve its compatibility with further computation and this modification has found its application in computing rational numbers, both recurring and terminating, with computational tile complexity of O 1 and O h respectively.…”

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confidence: 99%

Computing Real Numbers using DNA Self-Assembly

Shah,

Dave,

Gupta

2015

Preprint

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DNA Self-Assembly has emerged as an interdisciplinary field with many intriguing applications such DNA bio-sensor, DNA circuits, DNA storage, drug delivery etc. Tile assembly model of DNA has been studied for various computational primitives such as addition, subtraction, multiplication, and division. Xuncai et. al. gave computational DNA tiles to perform division of a number but the output had integer quotient [1]. In this work, we simply modify their method of division to improve its compatibility with further computation and this modification has found its application in computing rational numbers, both recurring and terminating, with computational tile complexity of O 1 and O h respectively. Additionally, we also propose a method to compute squareroot of a number with computational tile complexity of O n for an n bit number. Finally, after combining tiles of division and square-root, we propose a simple way to compute the ubiquitously used irrational number, π, using its GregoryLeibniz infinite series.

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“…Furthermore, we provided a scheme to factor the product of two prime numbers, and also designed protocols to execute integer factoring. 11 Graph theory has proven to be particularly useful to many diverse fields. The exciting and rapidly growing area of graph theory is rich in theoretical results as well as applications to real-world problems.…”

Section: Introductionmentioning

confidence: 99%

DNA Self-Assembly for Graph Vertex 3-Coloring Problem

Wang¹,

Hu²,

Shi³

et al. 2012

Jnl of Comp & Theo Nano

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This paper presents a method of DNA self-assembly for solving the graph vertex 3-coloring problem. We encode all vertices of a graph in DNA tiles as the inputs, and then assign colors to vertices based on the rule that two adjacent vertices can not be assigned the same color in the process of DNA self-assembly. By creating huge numbers of copies of the participating DNA tiles, the algorithm will run in parallel on all possible vertex 3-coloring situations, finally exclude the aborted coloring situations and obtain the successful vertex coloring scheme(s). The potential computations by DNA self-assembly for the vertex 3-coloring problem is promising given the operational time complexity of O n . This work shows further evidence for the ability of DNA self-assembly to solve other NP-complete problems.

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Arithmetic computation using self-assembly of DNA tiles: subtraction and division

Cited by 19 publications

References 22 publications

Toward Smart Information Processing with Synthetic DNA Molecules

Toward Smart Information Processing with Synthetic DNA Molecules

Computing Real Numbers using DNA Self-Assembly

DNA Self-Assembly for Graph Vertex 3-Coloring Problem

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