可交换上下文无关文法

本文提出了可交换上下文无关文法及其该文法产生的语言——可交换上下文无关语言，证明了正规语言类是可交换上下文无关语言类的一个子集，而可交换上下文无关语言类是上下文无关语言类的一个子集；讨论了可交换上下文无关语言的结构特点，并给出了可交换上下文无关语言的Pumping引理。     

量化上下文无关语言的代数性质

通过引入量化下推自动机与量化上下文无关文法的定义,研究了以两种不同方式接受语言的量化下推自动机等价性问题,证明了在可交换的双幺赋值幺半群上,量化下推自动机接受的语言与量化上下文无关文法生成的语言相同。     

一种有效的结点标号上下文无关图文法分析算法

本文讨论了上下文无关图文法的性质，并证明了图文法推导具有独立性．本文还给出了一种有效的上下文无关图文法分析算法，它具有多项式时间复杂性，并给出了算法的正确性证明．该算法已经用Ｃ语言实现．     

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。     

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.     

量子上下文无关文法的代数性质

提出了量子上下文无关文法（l-VCFG）的概念,并研究了其具有的代数性质;证明了量子上下文无关文法（l-VCFG）和Chomsky范式文法（l-VCNF）以及Greibach范式文法（l-VGNF）的相互等价性;详细研究了量子上下文无关语言的代数刻画以及对于正则运算的封闭性。     

格值树自动机与格值上下文无关树文法的等价性

本文将模糊树自动机和模糊上下文无关树文法的概念推广到格半群上。证明了在接受语言和生成语言的意义下,树自动机和上下文无关树文法是等价的。同时给出了构造正规形式的等价文法的方法。     

上下文无关语言的同步运算及其性质

针对上下文无关语言,引入了语言的可重复序列的依赖运算和同步运算,分析了两种运算的性质、特点,给出了可重复序列的依赖表达式、同步串约束表达式;提出了同步串约束上下文无关语言,给出了该类语言的构造规则:对于字母表上的同步串约束上下文无关语言L,都是由该字母表上的一个正规语言R与该正规语言R中某些可重复序列之间的依赖约束所形成的;证明了同步串约束上下文无关语言与同步串约束表达式所描述的语言等价,且该类语言是上下文无关语言的真子集.     

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。     

基于上下文无关文法的可逆变换模型

可逆变换和双向变换等数据转换问题一直是近年来的研究热点,研究人员针对该问题提出了大量相关的语言和模型。但是,这些实现往往建立在一种新的计算模型上,从而导致需要花费较大的学习成本去了解计算模型。另一方面,作为语法解析的基本工具,上下文无关文法对于绝大多数程序员来说都是不陌生的。提出了一种基于上下文无关文法的计算模型,用来构造字符串上的可逆变换,并对其性质和表达能力进行了探讨。采用Scheme语言实现了该计算模型,并通过在MIPS指令集上进行汇编和反汇编开发验证了该模型。验证结果表明,该模型具有较强的表达能力,在添加小型的公共数值变换模块后,可以完整地实现MIPS指令集上的汇编和反汇编。     

A generalization of leftmost derivations

A generalization of leftmost derivation called depth-first derivation is defined. The main result, that the depth-first derivations of an arbitrary phrase-structure grammar generate a context-free language, is proved using a new technique in which families of equivalent depth-first derivations of one grammar are represented by single productions in a new grammar. This result is related to several others, including an analogous result for leftmost derivations, through the theorem of B. Baker [1] that every terminal-bounded grammar generates a context-free language.     

Parikh?s theorem: A simple and direct automaton construction

Parikh?s theorem states that the Parikh image of a context-free language is semilinear or, equivalently, that every context-free language has the same Parikh image as some regular language. We present a very simple construction that, given a context-free grammar, produces a finite automaton recognizing such a regular language.     

Solutions of equations in languages

A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar has a unique solution. All this fits in an approach to search for a grammar for an arbitrary language that is given by other means. The approach is illustrated by the derivation of a grammar for a certain set of bit strings. The approach is used to give an elegant derivation of the grammar for a language accepted by a pushdown automaton.     

Controlled bidirectional grammars

We investigate context-free grammars the rules of which can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. We distinguish several modes of derivation for this kind of grammar. The resulting language families (properly) extend the family of context-free languages. We establish some closure properties of these language families and some grammatical transformations which yield a few normal forms for this type of grammar. Finally, we consider some special cases (viz. the context-free grammar is linear or left-linear), and generalizations, in particular, the use of arbitrary rather than regular control languages.     

Comprehension Grammars Generated from Machine Learning of Natural Languages

We are developing a theory of probabilistic language learning in the context of robotic instruction in elementary assembly actions. We describe the process of machine learning in terms of the various events that happen on a given trial, including the crucial association of words with internal representations of their meaning. Of central importance in learning is the generalization from utterances to grammatical forms. Our system derives a comprehension grammar for a superset of a natural language from pairs of verbal stimuli like Go to the screw! and corresponding internal representations of coerced actions. For the derivation of a grammar no knowledge of the language to be learned is assumed but only knowledge of an internal language.We present grammars for English, Chinese, and German generated from a finite sample of about 500 commands that are roughly equivalent across the three languages. All of the three grammars, which are context-free in form, accept an infinite set of commands in the given language.     

Context-free like restrictions on selective rewriting

Selective substitution grammars based on ‘context-free’ productions form a possible framework for the study of ‘grammatically oriented’ formal language theory. Such grammars (with no control governing the composition of derivation steps) are studied in this paper. In particular we study the effect of various conditions on selectors (which define the way that rewriting is performed); those conditions are aimed to formalize the notion of ‘using information about the context’ during the rewriting process. Each of them captures a particular feature of a rewriting according to a context-free grammar or an EOS system (essentially a context-free grammar that can also rewrite terminal symbols). Some of those conditions yield characterizations of the class of context-free languages for other conditions the lower and upper bound on the language generating power are given. Also a natural notion of a class of ‘simple’ rewriting systems is introduced (pattern grammars) and it is demonstrated that they possess surprisingly high language generating power.     

Left-forbidding cooperating distributed grammar systems

A left-forbidding grammar, introduced in this paper, is a context-free grammar, where a set of nonterminal symbols is attached to each context-free production. Such a production can rewrite a nonterminal provided that no symbol from the attached set occurs to the left of the rewritten nonterminal in the current sentential form. The present paper discusses cooperating distributed grammar systems with left-forbidding grammars as components and gives some new characterizations of language families of the Chomsky hierarchy. In addition, it also proves that twelve nonterminals are enough for cooperating distributed grammar systems working in the terminal derivation mode with two left-forbidding components (including erasing productions) to characterize the family of recursively enumerable languages.     

Dynamic LL(k) parsing

A new class of context-free grammars, called dynamic context-free grammars, is introduced. These grammars have the ability to change the set of production rules dynamically during the derivation of some terminal string. The notion of LL() parsing is adapted to this grammar model. We show that dynamic LL() parsers are as powerful as LR() parsers, i.e. that they are capable to analyze every deterministic context-free language while using only one symbol of lookahead. Received: 24 August 1994 / 5 January 1996     

On derivation languages corresponding to context-free grammars

Summary A derivation language associated with a context-free grammar is the set of all terminating derivations. Hierarchy and closure properties of these languages are considered. In addition to the formerly known solvability of the emptiness and finiteness problems the equivalence problem is shown to be solvable for derivation languages.