DNA computing是近幾年來利用分子生物來進行數學計算和邏輯運算的一個新研究領域。可以容易地實作出較暴力的演算法，來解決一些NP-complete的問題，如Hamiltonian path problem、traveling salesperson problem和satisfiability problem。也可以用來模擬目前電腦?娷眾瑼犒q路設計或晶片，如：簡單的1-bit比較器和加法器。這些主要是利用DNA可大量平行處理的特性。在本論文?堙A我們將利用DNA，首先設計出具有feedback能力的一個完整1-bit串流的比較器，其可完成兩個word的比較；再以此比較器為基本元件，完成一個生化的word-parallel bit-serial的排序器。事實上，我們排序器的設計方式，是可以應用在任何的sorting network來進行排序，例如：bitonic sorter和odd-even merge sorter。

In the past few years, several articles have been devoted to the study of molecular computing based on DNA in order to implement the algorithm to solve some NP-complete problems and simulate logic gates in silicon-based computers. A great deal of effort has been made on using DNA to implement simple logic gates, such as simple
1-bit comparators and simple adders, or to solve NP-complete problems, such as the Hamiltonian path problem, the traveling salesperson problem and the satisfiability problem. All of the methods rely on the capability of DNA computing which could perform computation in huge parallelism to produce all possible solutions where the answer may be derived from. In this thesis, we will first design a full bit-serial
comparator that can perform the feedback operation. Then, we will design a word-parallel bit-serial sorter which uses our comparators as the elementary building components. Our design of sorters can be applied to any sorting network, such as bitonic sorter and odd-even merge sorter.

TABLE OF CONTENTS
Page
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Chapter 2. Basic Operations of DNA Computing . . . . . . . . . . . . 4
Chapter 3. Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1 The Hamiltonian Path Problem Solved by Adleman . . . . . . . . . . 12
3.2 The Satis.ability Problem Solved by Lipton . . . . . . . . . . . . . . 14
3.3 Solid Phase DNA Solution for the Hamiltonian Path Problem . . . . 16
3.4 SAT’s Solution by HaoyangWu . . . . . . . . . . . . . . . . . . . . . 20
3.5 Amos’s NAND Boolean Circuits . . . . . . . . . . . . . . . . . . . . . 22
3.6 DNA Adders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 4. A Word-Parallel Bit-Serial Sorter . . . . . . . . . . . . . . 29
4.1 A Bit-Serial Comparator . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 The Encoding of the Comparator . . . . . . . . . . . . . . . . . . . . 31
4.3 How toMake the Biological SorterWork . . . . . . . . . . . . . . . . 36
4.4 Implementation of the Bitonic Sorters . . . . . . . . . . . . . . . . . 40
Chapter 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

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