Molecular Computation Based on Tile Assembly Model: Modular-Multiplication and Modular-Square over Finite Field GF(2N)

Li, Yongnan; Xiao, Limin

doi:10.1109/hpcc-smartcity-dss.2016.0143

Cited by 2 publications

(3 citation statements)

References 23 publications

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“…The authors of (Li, 2018;Li and Xiao, 2016;Li et al, 2016) state that the execution time for the multiplication over a field GFð2 n Þ is OðnÞ using the TAM system, which is equal to the execution time of our model. But in the TAM model, 7746 different tiles are needed to do the calculations, and as explained above this leads to great complexity of the implementation in the laboratory of the TAM model.…”

Section: Discussionmentioning

confidence: 95%

“…The proposed model presents several advantages over other models that have been widely studied and previously published, such as the Tile Assembling model (TAM) and the Sticker model (Roweis et al, 1998). All the arithmetic calculations covered by the TAM have been performed only in a theoretical way (e. g. Brun, 2007;Li et al, 2013aLi et al, , 2013bLi and Xiao, 2014;Li and Xiao, 2016;Li et al, 2016;Li, 2018;Li and Zhang, 2018). Li et al (Li et al, 2013b) designed a tile assembly system that, in theory, could compute a square over GFð2 n Þ, based on the condition that all DNA operations are perfect.…”

Section: Discussionmentioning

confidence: 99%

“…Winfree showed that DNA computation is Turing-universal and proposed that DNA self-assembly can be used to compute functions or assemble shapes (Winfree, 1996;Winfree et al, 1998;Rothemund et al, 2004). The introduced model by Winfree and colleagues, known as tile assembly model (TAM), has been considered to implement arithmetic over a finite field (Barua and Das, 2003;Li et al, 2013bLi et al, , 2016Li, and Xiao, 2014). TAM is based on the self-assembly of double-crossover DNA molecules (known as tiles) into a rectangular lattice, a pseudo-crystalline growth that occurs in the presence of an infinite supply of a finite number of tile types (Rothemund and Winfree, 2000;Jonoska et al, 2011).…”

Section: Dna Computing Modelsmentioning

confidence: 99%

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A new DNA-based model for finite field arithmetic

Jirón

Soto

Marín

et al. 2019

Heliyon

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A B S T R A C TA Galois field GFðp n Þ with p ! 2 a prime number and n ! 1 is a mathematical structure widely used in Cryptography and Error Correcting Codes Theory. In this paper, we propose a novel DNA-based model for arithmetic over GFðp n Þ. Our model has three main advantages over other previously described models. First, it has a flexible implementation in the laboratory that allows the realization arithmetic calculations in parallel for p ! 2, while the tile assembly and the sticker models are limited to p ¼ 2. Second, the proposed model is less prone to error, because it is grounded on conventional Polymerase Chain Reaction (PCR) amplification and gel electrophoresis techniques. Hence, the problems associated to models such as tile-assembly and stickers, that arise when using more complex molecular techniques, such as hybridization and denaturation, are avoided. Third, it is simple to implement and requires 50 ng/μL per DNA double fragment used to develop the calculations, since the only feature of interest is the size of the DNA double strand fragments. The efficiency of our model has execution times of order Oð1Þ and OðnÞ, for the addition and multiplication over GFðp n Þ, respectively. Furthermore, this paper provides one of the few experimental evidences of arithmetic calculations for molecular computing and validates the technical applicability of the proposed model to perform arithmetic operations over GFðp n Þ.

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Section: Discussionmentioning

confidence: 95%