基于Unsharp量子逻辑的自动机和文法理论

初步建立了具有某种分配律的扩展格序效应代数和格序QMV代数这两种unsharp量子结构上的自动机与文法理论的基本框架。引入了ε-值正则文法的概念,证明了任意ε-值自动机识别的语言等价于某种ε-值正则文法所生成的语言;反之,任意[ε]-值正则文法所生成的语言等价于某种ε-值自动机识别的语言。讨论了ε-值正则语言在和、连接及反转运算下的封闭性质。     

基于量子逻辑的自动机和文法理论

初步建立了基于量子逻辑的自动机和文法理论的基本框架.引入了量子文法(称为l值文法),特别是证明了任意l值正规文法生成的语言(称为量子语言)等价于某种基于量子逻辑且含动作(的自动机(称为l值自动机)识别的语言,反之,任意l值自动机识别的语言等价于某l值正规文法生成的语言.建立了l值泵引理,并得到量子语言的判定性刻画.最后简要讨论了正规文法与量子文法(即l值正规文法)的关系.因此,为进一步研究更复杂的量子自动机(如量子下推自动机和Turing机)和量子文法(如量子上下文无关文法和上下文有关文法)奠定了基础.     

Lukasiewicz逻辑值上下文无关语言的代数刻画

提出了基于Lukasiewicz逻辑的下推自动机（l-VPDA）的概念,从代数角度研究了此类自动机的性质,同时建立此类自动机的代数刻画,即利用模糊状态构造,证明了任意以终状态方式接受模糊语言的l-VPDA与状态转移为经典函数且具有l值模糊终状态的l-VPDA间的相互等价性;并证明任意以空栈方式接受模糊语言的l-VPDA与状态转移除一步转移为模糊的以外,其余都是经典函数的l-VPDA是相互等价的;详细研究了l-值模糊上下文无关语言的代数和层次刻画,以及对于正则运算的封闭性。     

基于量子逻辑的确定型正则文法

基于量子逻辑的文法理论是量子计算模型的一个重要研究方向.给出了基于量子逻辑的确定型正则文法的概念,证明了基于量子逻辑的确定型正则文法与基于量子逻辑的确定型自动机的等价性.利用此等价性,给出了量子确定正则语言的代数刻画和层次刻画,并得到量子确定正则语言关于正则运算的封闭性.     

取值于赋值幺半群的加权正则文法语言

正则文法是研究自动机的重要工具。引入取值于赋值幺半群的加权正则文法、加权类正则文法的定义,讨论了赋值幺半群上加权正则文法、加权类正则文法和加权有限自动机(WFA)的关系。证明了在赋值幺半群上,已知一个加权正则文法或加权类正则文法,分别存在一个WFA与之等价。定义了可分配的赋值幺半群,证明了在可分配的赋值幺半群上已知一个WFA,存在一个加权正则文法和加权类正则文法与之等价,即证明了可分配的赋值幺半群上加权正则文法、加权类正则文法和WFA在生成语言上等价,并举例说明了赋值幺半群的可分配性不是已知WFA存在与之等价的加权正则文法或加权类正则文法的必要条件。     

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。     

量子Müller自动机与单体二阶量子逻辑

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.     

基于量子逻辑的下推自动机与上下文无关文法

给出基于量子逻辑的下推自动机(e-VPDA)的概念,提出广义的子集构造方法,进而证明了一般的e-VPDA与状态转移为分明函数且具有量子终态的e-VPDA的等价性.利用此等价性,给出了量子上下文无关语言的代数刻画与层次刻画,并籍此证明了量子上下文无关语言关于正则运算的封闭性.最后,说明了量子下推自动机和量子上下文无关文法(e-VCFG)的等价性.     

模糊Büchi自动机的等价刻画

模糊语言的研究是形式语言研究的焦点之一,然而如何对模糊语言进行刻画甚至更好地分类是其中一个重要研究方向.文章在模糊ω-语言的研究基础上,从模糊逻辑角度研究了模糊ω-正则语言的等价刻画.首先借助广义子集构造方法,证明了任一模糊Büchi自动机与具有分明初始状态和状态转移函数且具有模糊终状态的模糊Büchi自动机是等价的,藉此研究了模糊ω-正则语言的代数刻画和层次刻画,讨论了模糊ω-正则语言关于正则运算的封闭性;其次引入单体二阶(L)ukasiewicz逻辑的概念,给出模糊Büchi自动机识别语言的等价逻辑刻画;最后通过引入ω-星自由和ω-非周期模糊ω-语言,利用“层次化”处理技巧得到了多值逻辑意义下的分类定理,对模糊ω-正则语言给出了一种分类方法.     

形式语言与自动机中关于ε的一些问题

讨论了形式语言与自动机理论中关于空串ε的一些问题。分析了ε产生式对文法和语言分类的影响;从文法和有限状态自动机的角度讨论了开始符号S和开始状态q0的作用;提出了语言增加或减少ε句子的简单方法;研究了ε-NFA的ε状态转换函数的本质;提出了ε-NFA转换为NFA的新方法,即先将ε-NFA转换为文法形式,消除ε产生式和单产生式后得到正则文法,再将正则文法转换为NFA。并用实际例子进行了验证。     

Controlled finite automata

This paper discusses finite automata regulated by control languages over their states and transition rules. It proves that under both regulations, regular-controlled finite automata and context-free-controlled finite automata characterize the family of regular languages and the family of context-free languages, respectively. It also establishes conditions under which any state-controlled finite automaton can be turned into an equivalent transition-controlled finite automaton and vice versa. The paper also demonstrates a close relation between these automata and programmed grammars. Indeed, it proves that finite automata controlled by languages generated by propagating programmed grammars with appearance checking are computationally complete. In fact, it demonstrates that this computational completeness holds even in terms of these automata with a reduced number of states.     

Context-free languages over infinite alphabets

In this paper we introduce context-free grammars and pushdown automata over infinite alphabets. It is shown that a language is generated by a context-free grammar over an infinite alphabet if and only if it is accepted by a pushdown automaton over an infinite alphabet. Also the generated (accepted) languages possess many of the properties of the ordinary context-free languages: decidability, closure properties, etc.. This provides a substantial evidence for considering context-free grammars and pushdown automata over infinite alphabets as a natural extension of the classical ones. Received November 27, 1995 / March 4, 1997     

On regular tree languages and deterministic pushdown automata

The theory of formal string languages and of formal tree languages are both important parts of the theory of formal languages. Regular tree languages are recognized by finite tree automata. Trees in their postfix notation can be seen as strings. This paper presents a simple transformation from any given (bottom-up) finite tree automaton recognizing a regular tree language to a deterministic pushdown automaton accepting the same tree language in postfix notation. The resulting deterministic pushdown automaton can be implemented easily by an existing parser generator because it is constructed for an LR(0) grammar, and its size directly corresponds to the size of the deterministic finite tree automaton. The class of regular tree languages in postfix notation is a proper subclass of deterministic context-free string languages. Moreover, the class of tree languages which are in their postfix notation deterministic context-free string languages is a proper superclass of the class of regular tree languages.     

Morphismes et bimorphismes d'arbres

For every pair of positive integers n and p, there is a language accepted by a real-time deterministic pushdown automaton with n states and p stack symbols and size O(np), for which every context-free grammar needs at least n²p+1 nonterminals if n>1 (or p non-terminals if n = 1). It follows that there are context-free languages which can be recognized by pushdown automata of size O(np), but which cannot be generated by context-free grammars of size smaller than O(n²p); and that the standard construction for converting a pushdown automaton to a context-free grammar is optimal in the sense that it infinitely often produces grammars with the fewest number of nonterminals possible.     

Approximation of fuzzy context-free grammars

Fuzzy context-free max- grammar (or FCFG, for short), as a straightforward extension of context-free grammar, has been introduced to express uncertainty, imprecision, and vagueness in natural language fragments. Li recently proposed the approximation of fuzzy finite automata, which may effectively deal with the practical problems of fuzziness, impreciseness and vagueness. In this paper, we further develop the approximation of fuzzy context-free grammars. In particular, we show that a fuzzy context-free grammar under max- compositional inference can be approximated by some fuzzy context-free grammar under max-min compositional inference with any given accuracy. In addition, some related properties of fuzzy context-free grammars and fuzzy languages generated by them are studied. Finally, the sensitivity of fuzzy context-free grammars is also discussed.