电子学报
電子學報
전자학보
ACTA ELECTRONICA SINICA
2013年
6期
1093-1100
,共8页
量子逻辑%量子Büchi自动机%量子无穷正则语言%代数刻画%单体二阶量子逻辑%Büchi定理
量子邏輯%量子Büchi自動機%量子無窮正則語言%代數刻畫%單體二階量子邏輯%Büchi定理
양자라집%양자Büchi자동궤%양자무궁정칙어언%대수각화%단체이계양자라집%Büchi정리
quantum logic%quantum Büchi automaton%quantum infinite regular language%algebraic characterization%monadic second-order quantum logic%Büchi theorem
提出量子Büchi自动机（简记为LVBA ）的概念，利用量子状态构造方法证明了一般LVBA与状态转移为经典函数的LVSBA间的相互等价性，籍此研究了量子无穷正则语言的代数刻画、层次刻画和Büchi刻画以及对于正则运算的封闭性；通过引入单体二阶量子逻辑（简记为LVMSO ）的概念，给出量子Büchi自动机所识别无穷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。
提齣量子Büchi自動機（簡記為LVBA ）的概唸，利用量子狀態構造方法證明瞭一般LVBA與狀態轉移為經典函數的LVSBA間的相互等價性，籍此研究瞭量子無窮正則語言的代數刻畫、層次刻畫和Büchi刻畫以及對于正則運算的封閉性；通過引入單體二階量子邏輯（簡記為LVMSO ）的概唸，給齣量子Büchi自動機所識彆無窮語言的單體二階邏輯描述，深化和推廣瞭量子邏輯意義下的Büchi基本定理。
제출양자Büchi자동궤（간기위LVBA ）적개념，이용양자상태구조방법증명료일반LVBA여상태전이위경전함수적LVSBA간적상호등개성，적차연구료양자무궁정칙어언적대수각화、층차각화화Büchi각화이급대우정칙운산적봉폐성；통과인입단체이계양자라집（간기위LVMSO ）적개념，급출양자Büchi자동궤소식별무궁어언적단체이계라집묘술，심화화추엄료양자라집의의하적Büchi기본정리。
The notion of quantum Büchi automaton (LVBA for short )is introduced ,by means of quantum state construction , the equivalence of an LVBA and an LVSBA with crisp transition function is proved ,based on this ,the algebraic and level character-izations and also the Büchi characterization of quantum infinite regular languages are investigated ,and also the closed properties of those quantum infinite regular languages under some regular operations are dealt with .By providing the concept of monadic second-order quantum logic (LVMSO in short ) ,the monadic second-order logic characterizations of infinite regular languages recognized by quantum Büchi automata are presented ,which deepen and generalize the fundamental Büchi theorem to quantum setting .
