利用剩余数制简化DNA算术运算

在DNA算术运算的理论模型中,普遍应用固定基数制,比如二进制、三进制。但是由于受到进位的影响,难以实现并行运算。基于Adleman-Lipton模型,分析了剩余数制的基本原理,改进了整数的DNA链表示,并将其应用于DNA算术运算,给出了剩余数制下进行DNA算术运算的算法模型。由于在剩余数制中,算术运算(加、减、乘)在剩余位之间无须进行进位计算,故可以降低运算过程的复杂度,而且有利于进行各个剩余位上的并行计算。

Simplify DNA arithmetic operation using residue number system

The fixed-base number system is widely implemented in the theoretical model of DNA arithmetic operation,such as binary number system,ternary number system.But the speed is limited by the carry-propagation of the weighted positional number system,the rippling effect on a sum makes it difficult to realize the arithmetic computation in parallel.In this paper,by analyzing the basic principle of Residue Number System(RNS),an improved DNA representation of number is presented and applied in the arithmetic computation based on the Adleman Lipton model,and the computing model and concrete procedure are presented.For the property of carry-free in RNS for arithmetic computation(addition,subtraction and multiplication),we can expect to decrease the complexity of computation,and utilize the advantage of parallelism of DNA computing sufficiently.