在這篇論文中，我們考慮兩個問題：(1)系統化的方法解決包含特殊性質的位元陣列 (2) 位元平行方法解決最近鄰居字串比對問題。對於問題(1)，我們假設一個陣列終止包含1和0，我們對找尋這個陣列中的一些特性有興趣。這些性質全都是涉及“所有”或“存在”的符號，我們對使用位元平行處理來找到這些性質感到興趣。在Myers的研究中，一連串的邏輯運算可以表示成一個邏輯公式：(∃k ≤ i, A(k) and ∀x∈[k, i – 1]) = (((A & B) + B) ^ B) | A)，這公式無庸置疑是不易求得的。我們研究的貢獻在於提出一個系統化的方法找到這樣的邏輯公式來解決包含“所有”和“存在”符號的位元陣列。藉由我們的思維方式，Myers所提出的公式可以一步步地被推導獲得。在這篇論文中我們定義了五個邏輯原型的問題： “單區間所有”、“單區間存在”、“多區間所有”、“多區間存在”和“多區間所有並存在”，並且證明這些問題全都可以利用位元平行運算在O(n/w) 的時間內完成（w為機器的字大小）。我們也考慮由這五種問題所延伸的四個變形，並證明它們的邏輯公式可以有系統地藉由五種問題原型獲得。最近鄰居字串比對問題定義如下：給定一本文字串T = t1t2…tn 以及一樣本字串 P = p1p2…pm，最近鄰居字串比對問題是去尋找到本文字串T當中所有的子字串與樣本字串P的編輯距離與其他子字串相比是最小。最近鄰居字串比對問題在生物資訊學上有相當有用的應用價值。最近鄰居字串比對問題可以直接利用處理近似字串比對的Seller和Myers演算法來解決。Hyyro和Navarro提出了過濾器演算法來加速Myers的演算法。然而，Hyyro和Navarro的過濾器方法需要建立基於近似字串比對問題所定義的誤差值k的預先處理。因此，它不適合於用來解決沒有定義誤差值k的最近鄰居字串比對問題。在這篇論文中，我們提出了Hyyro和Navarro演算法的修正版本，並且還提出結合Myers演算法和修正的Hyyro和Navarro演算法的位元平行演算法。在實驗中，我們亦證明了我們的位元平行演算法是有效率的。

In this thesis, we consider two problems: (1) Developing a systematical approach to solve problems involving special properties of bit-vectors (2) Developing a bit-parallel approach to solve the nearest neighbor string matching problem. For problem 1, suppose that we are given a vector consisting of only 1's and 0's and we are interested in finding some special properties of this vector. These properties all involve "for-all" or "there-exists" notations and we are interested in bit-parallel processes to find these properties. In Myers' work, a sequence of logical operations can be expressed as a logical formula: (∃k ≤ i, A(k) and ∀x∈[k, i – 1]) = (((A & B) + B) ^ B) | A) which is by no means easy to be obtained. The contribution of our research is to present a systematical method to find such logical formulas to solve problems involving bit vectors with "for-all" and "there-exists" notations. Using our way of thinking, the equation in Myers' work can be deduced step by step. Five logical prototype problems, "single-for-all", "single-there- exists", "multiple-for-all", "multiple- there-exists" and "multiple-there-exists-and-for-all", are defined in this thesis and are proved that all can be computed using bit-parallel operations in O(n/w) time, where w is the word size of the machine. We also consider four variants of the five problems and show that their logical formulas can be obtained using those of the five prototype problems systematically. The nearest neighbor string matching problem is defined as follows: Given a text string T = t1t2…tn and a pattern string P = p1p2…pm, the nearest neighbor string matching problem is to find all substrings of T whose edit distances with P are the smallest, among all substrings of T. The nearest neighbor string matching problem has useful applications in bioinformatics. It can be straight-forwardly solved by the Seller's Algorithm and the Myers Algorithm which are used to solve the approximate string matching problem. Hyyro and Navarro proposed a filtering algorithm to speed up the Myers Algorithm. However, Hyyro and Navarro's filtering approach needs to perform a pre-processing based on the error bound k which is given by the definition of approximate string matching problem. Hence, it is not suitable to be used to solve the nearest neighbor string matching problem which has no k. In this thesis, we present a modification of the Hyyro and Navarro Algorithm, and also present a bit-parallel algorithm combining the Myers Algorithm and the modified Hyyro and Navarro Algorithm. In experiments, we show that our bit-parallel algorithm is efficient.

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