Weng-Long Chang

Solving the set cover problem and the problem of exact cover by 3-sets in the adleman-lipton model

Adleman wrote the first paper in which it is shown that deoxyribonucleic acid (DNA) strands could be employed towards calculating solutions to an instance of the NP-complete Hamiltonian path problem (HPP). Lipton also demonstrated that Adlemans techniques could be used to solve the NP-complete satisfiability (SAT) problem (the first NP-complete problem). In this paper, it is proved how the DNA operations presented by Adleman and Lipton can be used for developing DNA algorithms to resolving the set cover problem and the problem of exact cover by 3-sets.

Fast parallel molecular solution to the dominating-set problem on massively parallel bio-computing

This paper shows how to use DNA strands to construct solution space of molecules for the dominating-set problem and how to apply biological operations to solve the problem from the solution space of molecules. In order to achieve this, we have proposed some DNA based parallel algorithms using the operations in Adleman-Lipton model, together with the analysis of the computational complexity for DNA parallel algorithms.

Fast Parallel DNA-Based Algorithms for Molecular Computation: The Set-Partition Problem

This paper demonstrates that basic biological operations can be used to solve the set-partition problem. In order to achieve this, we propose three DNA-based algorithms, a signed parallel adder, a signed parallel subtractor and a signed parallel comparator, that formally verify our designed molecular solutions for solving the set-partition problem.

Towards solution of the set-splitting problem on gel-based DNA computing

Adleman wrote the first paper that demonstrated that DNA (DeoxyriboNucleic Acid) strands could be applied for dealing with solutions of the NP-complete Hamiltonian path problem (HPP). Lipton wrote the second paper that showed that the Adleman techniques could also be used to solve the NP-complete satisfiability (SAT) problem (the first NP-complete problem). Adleman and his co-authors proposed sticker for enhancing the Adleman-Lipton model. In this paper, it proves how to apply sticker in the sticker-based model to construct solution space of DNA in the set-splitting problem and how to apply DNA operations in the Adleman-Lipton model to solve that problem from the solution space of sticker.

Quantum Algorithms for Biomolecular Solutions of the Satisfiability Problem on a Quantum Machine

In this paper, we demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented more efficiently by our proposed quantum algorithm on the quantum machine proposed by Deutsch. To test our theory, we carry out a three-quantum bit nuclear magnetic resonance experiment for solving the simplest satisfiability problem.

Molecular solutions of the RSA public-key cryptosystem on a DNA-based computer

The RSA public-key cryptosystem is an algorithm that converts a plain-text to its corresponding cipher-text, and then converts the cipher-text back into its corresponding plain-text. In this article, we propose five DNA-based algorithms—parallel adder, parallel subtractor, parallel multiplier, parallel comparator, and parallel modular arithmetic—that construct molecular solutions for any (plain-text, cipher-text) pair for the RSA public-key cryptosystem. Furthermore, we demonstrate that an eavesdropper can decode an encrypted message overheard with the linear steps in the size of the encrypted message overheard.

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

We propose three DNA-based algorithms - parallel subtractor, parallel comparator and parallel modular arithmetic - that formally verify our designed molecular solutions for factoring the product of two large prime numbers.

Fast Parallel DNA-Based Algorithms for Molecular Computation: Quadratic Congruence and Factoring Integers

Assume that is a positive integer. If there is an integer such that , i.e., the congruence has a solution, then is said to be a quadratic congruence . If the congruence does not have a solution, then is said to be a quadratic noncongruence . The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithms submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.

Solving the Independent-set Problem in a DNA-Based Supercomputer Model

In this paper, it is demonstrated how the DNA (DeoxyriboNucleic Acid) operations presented by Adleman and Lipton can be used to develop the parallel genetic algorithm that solves the independent-set problem. The advantage of the genetic algorithm is the huge parallelism inherent in DNA based computing. Furthermore, this work represents obvious evidence for the ability of DNA based parallel computing to solve NP-complete problems.

Fast parallel DNA-based algorithms for molecular computation: discrete logarithm

Diffie and Hellman (IEEE Trans. Inf. Theory 22(6):644–654, 1976) wrote the paper in which the concept of a trapdoor one-way function was first proposed. The Diffie–Hellman 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 Diffie–Hellman public-key cryptosystem is based on the difficulty of solving the problem of discrete logarithms. In this paper, we demonstrate that basic biological operations can be applied to solve the problem of discrete logarithms. In order to achieve this, we propose DNA-based algorithms that formally verify our designed molecular solutions for solving the problem of discrete logarithms. Furthermore, this work indicates that public-key cryptosystems based on the difficulty of solving the problem of discrete logarithms are perhaps insecure.