Studies On Some Generalized Disjunctive Languages And Generalized Regular Languages

In this thesis, we use mostly syntactic congruences and syntactic monoids to study some generalized disjunctive languages and generalized regular languages. First, by the theory of codes, we discuss the generalized disjunctive languages defined by prefix (suffix, bifix, infix, outfix) codes, and we give the disjunctive hierarchy of the class of these languages. Second, to answer the question(Is every relatively regular language can be decomposed as a union of a regular language and a thin language?) proposed by Liu yun in his Dr. thesis, we discuss some properties about the dense relatively regular languages, and give a equivalent description of the question.