# 臺灣博碩士論文加值系統

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 在本篇論文當中，我們首先介紹迴文的觀念和迴文演算法來解決字串中是否存在迴文的問題。接著我們提出三個方法，這三個方法都是用來建立字串，而這些字串都存在著某些特別的屬性。第一個方法產生出費氏序列的字串，而且擁有迴文和重複片段的屬性。第二個方法產生交替費氏序列屬性的字串。交替費氏序列屬性的定義如下： fn-2+fn-1和fn-1+fn-2 。最後我們定義區塊迴文的屬性如下：假設x是一個字串，xBR 就是x的區塊反轉，再假設S是一個序列，如果S是區塊迴文S=S1+S2 ,|S1|=|S2| ,S2 就是S1 的區塊反轉，而S1 和S2 就稱為區塊迴文。
 In this thesis, we first introduced the concept of palindromes and the Manacher algorithm to solve this problem. We then show words with special properties can be generated by generating functions. We proposed three generating functions. The first one generates Fibonacci words with properties concerning with palindromes and repeating groups. The second one generates a class of alternating Fibonacci words. That is, in this class, the words are alternatively fn-2+fn-1 and fn-1+fn-2. Finally we defined a class of words called block palindromes. Let x be a string. We shall use xBR to denote the block reverse of X. Let S be a sequence. S is a block palindrome if and only if S=S1+S2, |S1|=|S2| , S2 is a block reverse of S1 and both S1 and S2 are block palindromes. Our third generating function generates block palindromes.
 List of Figures vList of Tables viChapter 1 Introduction 1-11.1 The exact copy 1-11.2 The symmetric copy 1-1Chapter 2 The Manacher Algorithm 2-12.1 The Brute Force Algorithm 2-12.2 An Example of the Brute Force Algorithm 2-32.3 The Manacher Algorithm 2-42.4 An Example of Manacher Algorithm 2-10Chapter 3 Some Properties of Some Fibonacci Words 3-13.1 The Method 3-1 and Its Properties 3-13.2 The other Methods 3-6Chapter 4 Alternating Fibonacci Words 4-1Chapter 5 Block Palindrome 5-1Chapter 6 Conclusions 6-1Bibliography 7-1
 [H75] A Linear Space Algorithm for Computing Maximal Common Subsequences, Hirschberg D.S., Communications of the ACM, Vol. 18, No.6, June 1975, pp. 341-343.[LZ77] A universal algorithm for sequential data comression, Lempel, A. and Ziv, J., IEEE Transaction Information Theory, IT 23: 1977, pp. 337-343.[LZ78] Compression of individual sequences via variable-rate coding, Lempel, A. and Ziv, J., IEEE Transaction Information Theory, IT 24:, 978, pp.530-536.[W84] A technique for High-Performance Data Compression, Welch, T. A., IEEE Computer, Juan 1984, pp. 8-19.[M75] A new linear-time on-line algorithm for finding the smallest initial palindrome of the string, J. ACM 22, 1975, pp. 346-351.[BM77] A Fast String Searching Algorithm, Boyer, R. S. and Moore, J. S., Communication of the ACM, Vol. 20, 1977, pp. 762-772.[C92] String-Matching on Ordered Alphabets, Crochemore, M., Theoretical Computer Science, Vol. 92, 1992, pp. 33-47.[CP91] Two-Way String Matching, Crochemore, M. and Perrin, D., Journal of ACM, Vol. 38(3), 1991, pp.651-675.[CR2002] Jewels of Stringology, Crochemore, M. and Rytter, W., World Scientific, Singapore, 2002.[BS02] Algebraic Combinatorics on words, Berstel J. and Seebold P., 2002.[L97] Strumian words: structure, combinatorics, and their aritmetics, de Luca A., Theoretical Computer Science Vol. 183, 1997, pp.45-82.[DJP] Episturmian words and some constructions of de Luca and Rauzy, Droubay X, Justin J and Pirillo G., Theoretical Computer Science.[JP97] Decimations and Sturmian words, Justin J. and Pirillo G., Informatique theoriqueet Applications, Vol 31, 1997, pp. 271-290.[L82] Combinatorics on words, Lothaire M., Addison-Wesley, 1982
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