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Journal of Hunan University

DNA Computation for a Special Integer Planning Problem

Lin-Bo Jiang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

By using the method of 22 kinds of fluorescence labeling in experiment environment of the based-surface approach,a DNA computation based algorithm for solving the problem of special integer planning was proposed.We have introduced a method,in which the above problem transforms into a special-1,0 and 1 integer planning problem.The solution of the special integer planning problem has paved the way for the complete solution of integer planning problems.

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By using the method of 22 kinds of fluorescence labeling in experiment environment of the based-surface approach,a DNA computation based algorithm for solving the problem of special integer planning was proposed.We have introduced a method,in which the above problem transforms into a special-1,0 and 1 integer planning problem.The solution of the special integer planning problem has paved the way for the complete solution of integer planning problems.
Since triple-stranded DNA can be formed readily at any location in double-standed DNA with a homologous deoxyoligonucleotide in the presence of RecA-protein,it can be explored the possibility and feasibility to compute by this unique structure.In this paper the author shows that triple-stranded DNA structure mediated by RecA protein can be used for solving 0-1 integer programming problem.It can be solved the integer programming problem and satisfiability problem by this model.It can be transformed from integer programming problem and satisfiability problem to 0-1 integer programming problem.
In this paper, it is demonstrated that the DNA-based algorithm [Ho et al. 2005] for solving an instance of the clique problem to any a graph G = (V, E) with n vertices and p edges and its complementary graph G1 = (V, E1) with n vertices and m = (((n*(n-1))/2)-p) edges can be implemented by Hadamard gates, NOT gates, CNOT gates, CCNOT gates, Grover's operators, and quantum measurements on a quantum computer. It is also demonstrated that if Grovers algorithm is employed to accomplish the readout step in the DNA-based algorithm, the quantum implementation of the DNA-based algorithm is equivalent to the oracle work (in the language of Grover's algorithm), that is, the target state labeling preceding Grover,s searching steps. It is shown that one oracle work can be completed with O((2 * n) * (n + 1) * (n + 2) / 3) NOT gates, one CNOT gate and O((4 * m) + (((2 * n) * (n + 1) * (n + 14)) / 6)) CCNOT gates. This is to say that for the quantum implementation of the DNA-based algorithm [Ho et al. 2005] a faster labeling of the target state is attained, which also implies a speedy solution to an instance of the clique problem.
DNA computation could in principle solve the satisfiability (SAT) problem due to the operations in parallel on extremely large numbers of strands. We demonstrate some quantum gates corresponding to the DNA ones, based on which an implementation of DNA algorithm for SAT problem is available by quantum mechanical way. Since quantum computation owns the favorable feature of operations in parallel on 2n^{n}n states by using only n qubits, instead of 2n^{n}n strands in DNA computation, computational complexity is much reduced in treating the SAT problem quantum mechanically. We take a three-clause SAT problem with two variables as an example, and carry out a NMR experiment for solving a one-variable SAT problem.
We demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented by our proposed quantum algorithm on the quantum machine proposed by Deutsch. Moreover, we also prove that the logic computation by the bio-molecular operations proposed by Adleman can be implemented by quantum gates (for example, the Hadamard gate, NOT, CNOT, and CCNOT) on the quantum machine. Furthermore, those NP-complete problems solved on a bio-molecular computer are also solvable on a quantum computer. To test our theory, we carry out a three-qubit NMR experiment for solving the simplest satisfiability problem.