同步格值自动机的约简和最小化算法

引入了完备L-Fuzzy矩阵的概念,提出了取值于格半群上的输入字符和输出字符长度相同的模糊自动机的概念,即完备的同步格值自动机的概念,研究了它的主要性质;从行为矩阵出发,给出了完备的同步格值自动机状态等价和自动机等价的定义,从自动机的状态等价,研究了该自动机可约简的条件,并得到了该自动机的最小化算法。     

格值有限状态自动机的半群

提出了格值有限状态自动机的定义,给出了格值有限状态自动机的两种同余关系,研究了格值有限状态自动机的半群的若干性质,最后给出了两种有限半群E(A)和E(A)的关系。     

Mizumoto格值有限自动机及其最小化

提出取值为格半群的Mizumoto格值有限自动机的概念,得到基于模糊字符串的Mizumoto格值有限自动机的扩张模型,并详细讨论了其性质。同时建立了扩张Mizumoto格值有限自动机与标准扩张Mizumoto格值有限自动机的等价性,在此基础上给出了其最小化算法。     

一类格值自动机的极小化

给出了格值自动机的同余和同态,从代数角度出发详细研究了同余和同态关系的代数性质,揭示了格值自动机的代数性质和取值格半群的紧密联系,利用同余和同态关系最终研究了格值自动机的极小化问题,在正则同余下给出了可在有限步实现具有模糊初始状态和特殊模糊终状态的自动机极小化的算法。     

格值交替树自动机

交替（树）自动机因其本身关于取补运算的简洁性及其与非确定型（树）自动机的等价性,成为自动机与模型检测领域研究的一个新方向.在格值交替自动机与经典交替树自动机概念的基础上,引入格值交替树自动机的概念,并研究了格值交替树自动机的代数封闭性和表达能力.首先,证明了对格值交替树自动机的转移函数取对偶运算,终止权重取补之后所得自动机与原自动机接受语言互补这一结论.其次,证明了格值交替树自动机关于交、并运算的封闭性.最后,讨论了格值交替树自动机和格值树自动机、格值非确定型自动机的表达能力;证明了格值交替树自动机与格值树自动机的等价性,并给出了二者相互转化的算法及其复杂度分析;同时,提供了用格值非确定型自动机来模拟格值交替树自动机的方法.     

循环自动机的等价性

主要讨论了两个循环有限自动机的等价性与循环有限自动机的生成子之间的关系,在某些条件下给出了两个循环有限自动机等价的充分必要条件。     

格值下推自动机与格值上下文无关文法

引入了格值下推自动机、格值上下文无关文法及它们的语言的概念,证明了格值下推自动机以两种不同方式接受的语言类的等价性,研究了格值Chomsky范式文法、格值上下文无关文法及其派生所产生的语言的等价条件,揭示了在一定条件下,格值下推自动机接受的语言类与格值上下文无关文法产生的语言类的等价性,证明了有理格值语言均被格值下推自动机识别。     

格值有限状态自动机的同态和商自动机

提出了格值有限状态自动机（LFSA）的同态、强同态的概念,研究了LFSAs同态、强同态的若干性质。在LFSAs强同态的基础上,得到了LFSA的商自动机及其最小化自动机,刻画了商自动机的性质。     

格值模态命题逻辑及其完备性

文中以满足第一及第二无限分配律的完备格为工具,建立了格值模态命题逻辑的语义理论,并指出这种语义是经典模态命题逻辑语义理论及[0,1]值模态命题逻辑语义理论的共同推广.给出了QMR0代数的定义,并分别以Boole代数及QMR0代数为背景构建了Boole型格值模态命题逻辑系统B及QMR0型格值模态命题逻辑系统QML*,并证明了系统B及系统QML*的完备性.     

模糊Moore型自动机的性质(英文)

给出了模糊Moore型自动机可逆、可达和完备的定义;讨论了其相关性质,进而表明这些性质之间的关系,并且研究了模糊Moore型自动机的最小化性质。最后,系统地给出了关于它们的一些重要结果。     

Minimization of states in automata theory based on finite lattice-ordered monoids

In this study, we consider a concept of complete L-fuzzy matrix, define complete lattice-valued finite automata (CLFAs) and study their properties. The definitions of statewise equivalence relations and automata equivalence relations of a CLFA are given, two algorithms are aimed at the minimization of states of a CLFA.     

Regular grammars with truth values in lattice-ordered monoid and their languages

In this study, we introduce the concept of lattice-valued regular grammars. Such grammars have become a necessary tool for the analysis of fuzzy finite automata. The relationship between lattice-valued finite automata (LA) and lattice-valued regular grammars (LRG) are discussed and we get the following results, for a given LRG, there exists an LA such that they accept the same languages, and vice versa. We also show the equivalence between deterministic lattice-valued regular grammars and deterministic lattice-valued finite automata.     

Finite automata theory with membership values in lattices

In this paper, we study finite automata with membership values in a lattice, which are called lattice-valued finite automata. The extended subset construction of lattice-valued finite automata is introduced, then the equivalences between lattice-valued finite automata, lattice-valued deterministic finite automata and lattice-valued finite automata with ε-moves are proved. A simple characterization of lattice-valued languages recognized by lattice-valued finite automata is given, then it is proved that the Kleene theorem holds in the frame of lattice-setting. A minimization algorithm of lattice-valued deterministic finite automata is presented. In particular, the role of the distributive law for the truth valued domain of finite automata is analyzed: the distributive law is not necessary to many constructions of lattice-valued finite automata, but it indeed provides some convenience in simply processing lattice-valued finite automata.     

An overview of quantum computation models: quantum automata

Quantum automata, as theoretical models of quantum computers, include quantum finite automata (QFA), quantum sequential machines (QSM), quantum pushdown automata (QPDA), quantum Turing machines (QTM), quantum cellular automata (QCA), and the others, for example, automata theory based on quantum logic (orthomodular lattice-valued automata). In this paper, we try to outline a basic progress in the research on these models, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata. Also, other models closely relative to them are mentioned. In particular, based on the existing results in the literature, we finally address a number of problems to be studied in future.     

An overview of quantum computation models: quantum automata

Quantum automata, as theoretical models of quantum computers, include quantum finite automata (QFA), quantum sequential machines (QSM), quantum pushdown automata (QPDA), quantum Turing machines (QTM), quantum cellular automata (QCA), and the others, for example, automata theory based on quantum logic (orthomodular lattice-valued automata). In this paper, we try to outline a basic progress in the research on these models, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata. Also, other models closely relative to them are mentioned. In particular, based on the existing results in the literature, we finally address a number of problems to be studied in future.     

右线性文法与有限自动机等价性的一个新证明

迄今为止,左、右线性文法与有限自动机的等价性都是通过相互模拟构造来证明的。文章首先引入字母表上的右线性方程组及其最小解的概念,证明了最小解的存在性与有效可解性,描述了最小解的结构;其次通过右线性方程组及其最小解,证明了右线性文法与有限自动机的等价性。完全类似地,可以引入字母表上的左线性方程组及其最小解,并且证明左线性文...