中文摘要：

给出量子Müller自动机（简称LVMA）的概念，通过引入量子有限步可识别语言和量子状态构造方法，证明了在量子逻辑意义下4类量子Müller自动机彼此相互等价，利用该等价性，建立了量子无穷正则语言的代数刻画和层次刻画，籍此研究了量子无穷正则语言关于无穷正则运算的封闭性．同时，给出了量子Müller自动机所识别语言的单体二阶逻辑描述，深化和推广了量子逻辑意义下的Büchi基本定理．

英文摘要：

This paper introduces the notion of quantum Miiller automaton （LVMA）, provides the concept of quantum recognizable finite step language and the means of quantum state construction, and then proves the fact that four types of LVMA can equivalently constructed from each other. By using those equivalent relations, it establishes the algebraic and level characterizations of quantum regular infinite languages, and also explores the closed properties of these quantum infinite languages in details under some infinite regular operations in particular at the same time. Meanwhile, this study shows that the behaviors of quantum Mtlller automata are precisely the quantum languages definable with sentences of the monadic second-order quantum logic （LVMSO）, expanding the fundamental Biichi theorem to quantum setting.