近年來，DNA計算是一種常被用來解決NP-Complete問題的好用工具之一。DNA計算所具備的主要優點有大量的儲存空間以及平行計算的能力。在DNA計算的方面，已經採用暴力法來實際解決一些難題，如銷售旅行員問題和漢彌爾頓迴圈問題。當DNA計算在進行時，所有的解答都被儲存在試管中。然而，要在眾多的解答中找出正確的解答並不是一件相當容易的事，因為正確的解答的量跟其它的解答比起來可能微不足道，而在這篇論文中，我們所想要做的就是把正確解答的濃度加以提昇，以達成錯誤容忍的目標。

Recently, DNA computing is one of powerful tools that can be designed for solving NP-complete problems. The powers of DNA computing are that it has great ability of massive data storage and it can process those data in parallel. Some of hard problems, such as the traveling salesperson problem and the Hamiltonian cycle problem, have been solved with the brute force method in DNA computing. After DNA computing is performed, all feasible solutions for the problem are stored implicitly in the tubes. However, the correct answer still cannot be extracted or reported absolutely, because that the concentration of the correct solutions might be lower than other bad solutions. In this paper, we will increase the concentration of the correct answer for fault-tolerant ability.

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Some Useful Bio-chemical Experiment Methods in DNA Computing .............5
2.2 The Hamiltonian Path Problem . . . . . . . . . . . . . . . . . ... . . . 12
2.3 Logical Operations of Gene Expression . . . . . . . . . . . . .. . . . . 16
Chapter 3. A Minimum Finding Algorithm . . . . . . . . . . ......... . . . . 23
3.1 Minimum Finding in a Parallel System . . . . . . . . ... . . . . . . . . 23
3.2 Minimum Finding with DNA Computing . . . . . . ....... . . . . . . . . . 24
3.3 Global View . . . . . .. . . . . . . . . . . ... . . . . . . . . . . . . 30
3.4 The DNA Encoding Forms of Binary Values ...... . . . . . . . . . . . . . 30
3.5 Simulation and Analysis . . . . . .... . . . . . . . . . . . . . . . . . 34
Chapter 4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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