Computing Real Numbers using DNA SelfAssembly
Abstract
DNA SelfAssembly has emerged as an interdisciplinary field with many intriguing applications such DNA biosensor, 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 squareroot of a number with computational tile complexity of $\mathcal{O} (n)$ for an n bit number. Finally, after combining tiles of division and squareroot, we propose a simple way to compute the ubiquitously used irrational number, $\pi$, using its infinite series.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 arXiv:
 arXiv:1502.05552
 Bibcode:
 2015arXiv150205552S
 Keywords:

 Computer Science  Emerging Technologies
 EPrint:
 21 pages, draft