The DNA-Based Algorithms of Implementing Arithmetical Operations of Complex Vectors on a Biological Computer.

Here we show that arithmetical operations of complex vectors can be implemented by means of the proposed DNA-based algorithms.

Fast parallel molecular algorithms for DNA-based computation: factoring integers.

The RSA public-key cryptosystem is an algorithm that converts input data to an unrecognizable encryption and converts the unrecognizable data back into its original decryption form. The security of the RSA public-key cryptosystem is based on the difficulty of factoring the product of two large prime numbers. This paper demonstrates to factor the product of two large prime numbers, and is a breakthrough in basic biological operations using a molecular computer.

Fast parallel molecular solutions for DNA-based supercomputing: the subset-product problem.

In this paper our main purpose is to give molecular solutions for the subset-product problem. In order to achieve this, we propose three DNA-based algorithms--parallel adder, parallel multiplier and parallel comparator--that formally verify our designed molecular solutions for the subset-product problem. We also show that Boolean circuits are not needed to perform mathematical operations on a molecular computer.

Molecular solutions for the subset-sum problem on DNA-based supercomputing.

In this paper our main purpose is to give molecular solutions for the subset-sum problem. In order to achieve this, we propose a DNA-based algorithm of an n-bit parallel adder and a DNA-based algorithm of an n-bit parallel comparator to formally verify our designed molecular solutions for the subset-sum problem.