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.     

基于完备剩余格值逻辑的自动机和文法理论

初步建立基于完备剩余格值逻辑自动机与文法理论的基本框架。引入l值正则文法的概念,证明了任意l值自动机识别的语言等价于某种l值正则文法所生成的语言,反之,任意l值正则文法所生成的语言等价于某种l值自动机识别的语言。获得l值自动机及被l值自动机识别的语言的连接问题刻画。特别地,建立l值和L值泵引理,并得到l值语言的判定性刻画。最后,揭示带ε移动的l值自动机与不带ε移动的l值自动机之间的两个等价关系。     

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.     

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。     

正规文法与有限自动机的等价构造

在功能上,正规文法与有限自动机描述和识别语言是等价的,它们之间也存在等价构造算法,但这些构造算法有些复杂.对其算法进行了简化且给以了证明,并提出了一个从有限自动机构造等价左线性正规文法的算法,同时也进行了证明,最后给出了该算法的一个实例.     

语言{InIn》=1}的一个文法描述

介绍了一个描述语言{InIn>=1}的文法.     

正规文法与有限自动机的等价性研究

通过证明正规文法和有限自动机之间的等价性定理,给出正规文法和有限自动机之间的等价构造方法。     

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。     

语言{I^n^3ln〉=1}的一个文法描述

介绍了一个描述语言{I^n^3ln〉=1}的文法。     

FORTRAN语言的一个属性文法

本文介绍了用属性定义语言ALADIN写的FORTRAN语言的属性文法。该文法描述了FORTRAN语言的语法结构及其静态语义,包括作用域规则、说明的建立、表达式分析和出错处理等。     

模糊有穷自动机与单体二阶Lukasiewicz逻辑

该文引入了单体二阶Lukasiewicz逻辑,进而给出了模糊有穷自动机识别语言的逻辑描述,证明了多值逻辑意义下的Bchi与Elgot基本定理.通过引入星-自由模糊语言与非周期模糊语言,刻画了可以用一阶Lukasiewicz逻辑定义的模糊语言.     

A characterization of Büchi tree automata

We show that a language of infinite binary trees is definable by a Σ₂-formula of the monadic second order logic of two successors (with no additional symbols) iff it can be accepted by a Büchi automaton. The same result has been obtained by G. Lenzi, but our proof is simpler.     

Learning Syntax by Automata Induction

In this paper we propose an explicit computer model for learning natural language syntax based on Angluin's (1982) efficient induction algorithms, using a complete corpus of grammatical example sentences. We use these results to show how inductive inference methods may be applied to learn substantial, coherent subparts of at least one natural language — English — that are not susceptible to the kinds of learning envisioned in linguistic theory. As two concrete case studies, we show how to learn English auxiliary verb sequences (such as could be taking, will have been taking) and the sequences of articles and adjectives that appear before noun phrases (such as the very old big deer). Both systems can be acquired in a computationally feasible amount of time using either positive examples, or, in an incremental mode, with implicit negative examples (examples outside a finite corpus are considered to be negative examples). As far as we know, this is the first computer procedure that learns a full-scale range of noun subclasses and noun phrase structure. The generalizations and the time required for acquisition match our knowledge of child language acquisition for these two cases. More importantly, these results show that just where linguistic theories admit to highly irregular subportions, we can apply efficient automata-theoretic learning algorithms. Since the algorithm works only for fragments of language syntax, we do not believe that it suffices for all of language acquisition. Rather, we would claim that language acquisition is nonuniform and susceptible to a variety of acquisition strategies; this algorithm may be one these.     

On the structure of graphs in the Caucal hierarchy

We investigate the structure of graphs in the Caucal hierarchy. We provide criteria concerning the degree of vertices or the length of paths which can be used to show that a given graph does not belong to a certain level of this hierarchy. Each graph in the Caucal hierarchy corresponds to the configuration graph of some higher-order pushdown automaton. The main part of the paper consists of a study of such configuration graphs. We provide tools to decompose and reassemble their runs, and we prove a pumping lemma for higher-order pushdown automata.     

Recognisability for algebras of infinite trees

We develop an algebraic language theory for languages of infinite trees. We define a class of algebras called ω-hyperclones and we show that a language of infinite trees is regular if, and only if, it is recognised by a finitary path-continuous ω-hyperclone.     

二元文法

在正规文法的基础上,通过增加一个约束变量集合,给出了二元文法的定义,证明了二元文法与袋自动机的等价性,定义了平衡推导、递增推导、递减推导和传递推导,证明了它们与不变重复序列、增重复序列、减重复序列和传递重复序列之间的关系,并且给出判定一个二元文法所产生语言（袋语言）分别是正规语言、上下文无关语言或上下文文有关语言的充分条件。     

混合投影时序逻辑与混合系统的形式化验证

为了描述混合系统的性质和行为,10多年来,各种时序逻辑,如Hybrid Temporal Logic等相继出现。这些时序逻辑适用于刻画混合系统的性质和规范,但不适宜表示描述系统的实现模型。本文定义了一个混合投影时序逻辑（Hybrid Projection Temporal Logic,简称HPTL）,既能刻画混合系统的性质,又能表示混合系统的实现。这样,混合系统的验证就可以很方便地在统一的数学模型框架下进行。同时,给出了HPTL的基本的逻辑等价式系统和一个用HPTL进行混合系统验证的实例。