2026-11-092026-11-09https://scholars.csmu.edu.tw/handle/123456789/38763The theory of formal languages plays a considerable role in the field of computer science. Both regular languages and disjunctive languages are especially important applications. To simplify the judgment of disjunctivity of a language immediately, Ries and Shyr indicate that every disjunctive language is dense. The characteristic of dense provides the method to check whether a language is disjunctive. This study motivates the investigation of dense property of a language. To compare the dense property of a language, we will study the autodense languages which has the dense property, that is, every dense language is autodense. In the meanwhile, if the set is not an autodense language which will cover all the infix codes, then we define the set as the anti-autodense languages. We will study some algebraic properties concerning autodense languages and anti-autodense languages in this project. There is to investigate whether a subset of autodense or anti-autodense languages still contain autodense or anti-autodense property or not. We also investigate whether the finite union of autodense or anti-autodense languages is autodense or anti-autodense or not. Furhtermore, Are the family of autodense or anti-autodense languages closed under the catenation operation? Since the anti-autodense language covers all the infix codes, the relationships will be studied between anti-autodense languages and difference codes such as comma-free codes, intercodes, pure codes, etc. Finally, a procedure will be provided to construct an autodense or anti-autodense languages in this project.在資訊科學研究的領域中，正規化言語的理論扮演著重要的角色，其中對於規則化言語及分離化言語的研究就佔有相當大的部分。為了簡化判斷言語是否具有分離化的特性，在Ries及Shyr的研究中，提供了利用言語稠密的特性來判斷一個言語是否具有分離化性質的方法，此乃引起研究者對於一個言語其所含稠密化性質的研究興趣。 相較於言語稠密的特性，本研究乃是探討言語所具自動稠密的性質，使得含有自動稠密性的言語必包含有稠密的特性。同時，對於不具有自動稠密性質的言語，如果其能具有中置數碼的特性時，則此言語則是被定義為反自動稠密性言語，此類言語的性質也將是本研究所要探討的主軸。 對於自動稠密性及反自動稠密性言語，本研究計畫將就此二言語分別討論其所具有的代數性質，包括探討其子言語及多個言語聯集後是否會改變其自動稠密或反自動稠密的性質，並且對於連鎖的運算能否保持其封閉性等加以討論。其中，因反自動稠密性言語含有中置數碼的特性，所以本研究也將探討此言語與不同數碼（如：逗號自由數碼、中間數碼、純正數碼等）之間的關聯性。最後，於探究以上所提出之性質後，本研究將提出一個能夠建構具有自動稠密性及反自動稠密性言語的程序。規則化言語分離化言語中置數碼逗號自由數碼中間數碼純正數碼Regular languagesDisjunctive languagesInfix codesComma-free codesIntercodesPure codesProject