DNA modular subtraction algorithm based on linear self-assembly

This paper presents a DNA algorithm based on linear self-assembly which gives the result of the modular subtraction operation of two nonnegative integers. For two n-bit nonnegative integers A and B, the algorithm gives the result of A-B mod 2n. An extended borrow tag which indicates the relation of the minuend and the subtrahend is included in the resulting strand so that the pre-classification based on A>B or B>A is not required before the experiment. From the resulting strand, we can draw the information of operation result, operands, borrow, and the tag of the relation between the minuend and the subtrahend. The algorithm takes advantage of the parallelism characteristic of DNA computing: while given two sets of operands (one the minuend set and the other subtrahend set), the modular subtraction operation of these two sets can be achieved by a parallel processing procedure. The feasibility of the algorithm is based on a known experiment. The algorithm is of spontaneous characteristic which prevents the scale of the experimental procedures from growing with the length of the operands. As for the length of the operands n, there are O(n) kinds of strands required in the experiment, and the biochemical experimental procedures can be accomplished in constant number of steps.