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

Recently, experiments have demonstrated that simple binary arithmetic and logical operations can be computed by the process of self-assembly of DNA tiles. In this paper, we show how the tile assembly process can be used for subtraction and division. In order to achieve this aim, four systems, including the comparator system, the duplicator system, the subtraction system, and the division system, are proposed to compute the difference and quotient of two input numbers using the tile assembly model. This work indicates that these systems can be carried out in polynomial time with optimal O(1) distinct tile types in parallel and at very low cost. Furthermore, we provide a scheme to factor the product of two prime numbers, and it is a breakthrough in basic biological operations using a molecular computer by self-assembly.