言語(languages)與數碼(codes)在電算科學及資訊科學上擔一重要之角色。本文之目在探討一些言語與數碼的性質以利其在領域上之應用及分析。
令x為一有限字母(finite alphabet)之集合,x為由x所產之具有單位元素之自由半群(monoid),任x之子集合稱為一言語。令s為x中之一非空言語稱它為控制言語(control language)對於任一非空言語a,我們定義兩等價關係(equivalence relations)s及s,利用此兩等價關係,正則言語(regular languages),右析言語(right disjunctive languages)及析取言語(disjunctive languages)可推廣為s正則言語(s-regular languages),s右析取言語(s-disjunctive languages)及析取言語(s-disjunctive languages)。我們就控制言語s為任意集合,s為所有原始字(primitive words)之集合q及s為一厘想集合(ideal)時探討其一些性質。
再者,我們在x上定義了三種半序。利用這些半序可定義不同類型之曲言語(convex languages)獨立言語(independent languages),我們並加討論其諸性質。
我們亦探討一些數碼之性質與上述言語之關係。
最後,我們探討一些有關言語之自由半群的性質。我們得證在言語之自由半群中,每一個自由子半群if(free subsemigroup)若其基底(base)為一無限集合時皆可表為無限多個互不相交之if之自由子半群的聯集。某些特殊類型言語的性質亦討論之。

封面及摘要
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
chapter1 preliminaries
1.1 FUNDAMEMTALS AND NOTATIONS
1.2 SOME PROPERTIES OF PRIMITIVE WORDS,CODES AND MONOIDS
1.3 RELATIONS,AUTOMATA AND REGULAR LANGUAGES
chapter2 s-regular languages and codes
2.1 DEFINITIONS AND PROPERTIES OF S-REGULAR LANGUAGES
2.2 REGULAR LANGUAGE AND PREFIX CODES
2.3 S-REGULAR LANGUAGES AND HOMOMORPHISMS
2.4 S-STRONG CODES
chapter3 s-disjunctive languages
3.1 PRELIMINARIES
3.2 Q-DISJUNCTIVE LANGUAGES AND Q-RIGHT DISJUNCTIVE LANGUAGES
3.3 DISJUNCTIVE PAIRS AND S-DISJUNCTIVE PAIRS
3.4 SOME PROPERTIES OF DISJUNCTIVE LANGUAGES
chapter4 languages defined by relations
4.1 PRELIMINARIES
4.2 INDEPENDENT LANGUAGES
4.3 CONVEX LANGUAGES
4.4 POWERS AND STRICT POWERS OF LANGUAGES DEFINED BY PARTIAL ORDERS
chapter5 free semigroups of languages and some special classes of languages
5.1 PRCLIMINARIES
5.2 SOME FILTERS AND FREE SEMIGROUPS OF LANGUAGES
5.3 HAPPINGS AND FREE SUBSEMIGROUPS OF A FREE SEMIGROUP OF LANGUAGES
5.4 SOME PROPERTIES OF SOME SPECIAL CLASSES OF LANGUAGES
Bibiography
VITA