Research On The DNA Words And Its Arithmetic Actualize

With the rapid development of biological techniques, a new discipline named DNA computing has come into being. Owing to massive parallelism, high-density storage and low energy cost DNA computer overcome the disadvantages of electronic computer. This paper mainly focuses on the following two subjects: the encoding problem and DNA computing algorithm for the minimum vertex cover problem.Encoding problem is the key to DNA computing, so also the most difficult problem because it has not a general solution. In this thesis, we propose an efficient algorithm of constructivity based on linear codes .Our work is based on the work of Braich etal., in which they proposed a constraint condition model to produce DNA sequences through tertiary strands. Our proposed algorithm surpasss the search algorithm. The algorithm can fast and effieciently produce words with enough amount and high quality. So, it had solved the encoding problem with ternary alphabet.Given the word amount, we search the optimization encoding parameters such as words length l and maximum substring length s and minimum hamming distance d_h So, in this situtation we need only researching the words count. Now there are reports on the words count problem under single constraint, but up to now there is no report on this problem under multiple contraints. Our method had solved a multiple constraints words count problem which reckons words amount availably.Our result shows that search space optimazation is the key for finding H matrix with uniform distribution. The H matrix determines DNA code words weight distribution. When DNA code words scale less than 180, the encoding parameters currently is l=10-14, s=4-6, d_h=5-6, GC%≈1/3.Finally, we propose a DNA algorithm model for the minimum vertex cover problem based on satisfiable solution space, which can simplify process of DNAcomputing. It can also enlarge problem size simply through increasing the DNA solution.