利用DNA自组装计算实数
Computing Real Numbers using DNA Self-Assembly
摘要:
DNA自组装是一个多学科交叉的领域,具有许多有趣的应用,如DNA生物传感器,DNA电路,DNA存储,药物输送等。Tile组装模型的DNA已经研究了各种计算原语,如加,减,乘,除。Xuncai et.等人给出了计算DNA瓦片来执行数的除法,但输出具有整数商。在这项工作中,我们简单地修改了他们的除法,以提高其兼容性,进一步的计算和这种修改已发现其应用在计算有理数,循环和终止,计算瓦片的复杂性分别为$\mathcal{O} (1)$和$\mathcal{O} (h)$。此外,我们还提出了一种方法来计算一个数的平方根的计算瓦片的复杂性为$\mathcal{O} (n)$的n位数。最后,在结合了除法和平方根之后,我们提出了一种简单的方法来计算普遍使用的无理数$π$,使用它的无穷级数。
英文摘要:
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. 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 $\mathcal{O} (1)$ and $\mathcal{O} (h)$ respectively. Additionally, we also propose a method to compute square-root of a number with computational tile complexity of $\mathcal{O} (n)$ 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 infinite series.
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