EGG图文法语法分析算法的研究

EGG是一种基于边的上下文相关图文法形式化框架,其语法分析(归约操作)算法是该文法重要的组成部分。在简要介绍EGG的基础上,给出了EGG语法分析算法的设计,其中包括子图匹配算法、子图替换算法和算法计算复杂性的分析。为了展示如何用EGG来定义图语言,特别是如何用所设计的归约算法来分析图,文中以程序流程图为例,给出了相关的EGG形式定义以及对一个具体流程图的归约过程,并探讨了可能降低分析算法复杂性的一些途径。     

图文法综述

形式语言理论对计算机科学的发展起了重大的作用,作为对传统字符文法扩展的图文法的形式化研究,其重要意义是不言而喻的.本文在概述图文法的产生、发展和现状的基础上,着重介绍了从一维字符文法扩展到二维图文法所出现的新问题,以及在形式化处理上引出的新方法,其中最主要的是嵌入问题的解决、文法类型的划分和成员问题的判定.文中以目前较为流行的图文法为例,特别是一些典型的上下文无关和上下文相关的图文法,对上述的问题进行了深入的讨论,指出了现有方法中的一些不足之处,并展望了图文法今后值得研究的问题和方向.     

基于边的图文法产生式选择无关条件的判断

为了降低归约算法的时间复杂度,在基于边的上下文相关图文法(EGG)形式化的基础上,通过对产生式形式的适当约束,提出了EGG的产生式选择无关条件的判断方法。通过此方法可有效判断EGG产生式的选择无关性。对于选择无关的产生式,由于归约过程中产生式的使用顺序不会影响归约的结果,从而避免了回溯,能够有效地降低归约算法的时间复杂度。     

软件图语言的形式描述

本文从语言学和形式化角度对软件领域中广泛使用的软件图进行了研究，提出了软件图语言这一概念。本文首先提出了关于软件图语言的一组基本概念，其次研究软件图语言的同态和同构，以构成软件图形式描述的基础；最后讨论了软件图语言的形式表示法，并提出了基于图符网的文法，使图文法更适合于表示软件图语言。本文工作可以作为设计面向软件图语言的软件工具的基础。     

On the Expressiveness of Context-Sensitive Graph Grammars

上下文相关图文法是描述可视化语言的形式化工具.为了直观地刻画并高效地分析可视化语言,已有图文法形式框架均着重于文法形式和分析算法的研究,而忽略了对它们之间表达能力的分析.在对已有上下文相关图文法形式框架的关键特征进行分析和归纳的基础上,通过构造不同形式框架之间的转换算法,揭示并形式化证明了它们表达能力之间的关系.而且,转换算法在不同形式框架之间建立了关联,使图文法的应用不必再局限于一个框架,而是可以选择不同框架分别进行图的描述和分析,从而提高了上下文相关图文法的易用性.     

上下文相关图文法的表达能力分析

上下文相关图文法是描述可视化语言的形式化工具.为了直观地刻画并高效地分析可视化语言,已有图文法形式框架均着重于文法形式和分析算法的研究,而忽略了对它们之间表达能力的分析.在对已有上下文相关图文法形式框架的关键特征进行分析和归纳的基础上,通过构造不同形式框架之间的转换算法,揭示并形式化证明了它们表达能力之间的关系.而且,转换算法在不同形式框架之间建立了关联,使图文法的应用不必再局限于一个框架,而是可以选择不同框架分别进行图的描述和分析,从而提高了上下文相关图文法的易用性.     

一种基于边的上下文相关图文法形式化框架

围绕解决图文法中的主要问题——嵌入问题,提出了一种基于边的上下文相关图文法形式化框架,并对由此定义的文法的一些性质及相应的归约算法进行了讨论.对所提出的图文法与已有的文法进行了比较.同时,展望了今后值得进一步研究的一些问题和方向.     

vCGG:一种基于虚结点的空间图文法形式框架

作为一种二维的形式化方法,图文法为可视化语言提供了直观而规范的描述手段.然而,大多数图文法形式框架在空间语义处理能力方面有所不足,影响了图文法的表达能力及其实际应用范围.针对现存的问题,构建了一种新型空间图文法形式框架vCGG （virtual-node based coordinate graph grammar）.区别于其他空间图文法,vCGG在产生式中通过定义虚结点的概念描述产生式与主图之间的语法结构与空间语义关系,在保留抽象能力的同时,提高了其空间语义配置性能.通过与几种典型空间图文法框架比较,vCGG形式框架在直观性、规范性、表达能力以及分析效率方面均有着较好的表现.     

嵌入一致图语法的依赖图

图语法将字符串上的形式文法扩充为图上的形式文法,提供一种能够使用精确的数学方法来模拟图变换的机制.提出了几种新的基于一致图语法的方法来表示控制流图、数据流图、控制数据流图、二分图和超图,并说明如何通过图重写来自动生成依赖图并挖掘并行性,从而协助并行编译器和并行语言的设计和实现.     

上下文相关图文法分析及其应用初探

图文法是一种对可视化语言进行形式化定义的元语言，具有表达自然、能力强大的特点.随着使用可视化语言的最终用户编程技术的广泛应用，图文法分析尤其是上下文相关图文法分析在工程应用中的重要性日益突出.国内外相关文献或着重于纯理论探讨，或局限于特定语法类的特定应用，不利于工程应用人员参考.本文选取简洁明了的符号体系，介绍上下文相关图文法分析的一般性过程，并将其中规则选取关键步骤描述为CSP问题，利用已有的针对CSP问题的优化方法来优化算法，介绍了现有的优化方法并给出实现算法;同时，结合自身实践，讨论其在一个面向体系结构的Web服务集成系统中的应用.     

A Query Language for XML Based on Graph Grammars

In this paper we present a graphical query language for XML. The language, based on a simple form of graph grammars, permits us to extract data and reorganize information in a new structure. As with most of the current query languages for XML, queries consist of two parts: one extracting a subgraph and one constructing the output graph. The semantics of queries is given in terms of graph grammars. The use of graph grammars makes it possible to define, in a simple way, the structural properties of both the subgraph that has to be extracted and the graph that has to be constructed. We provide an example-driven comparison of our language w.r.t. other XML query languages, and show the effectiveness and simplicity of our approach.     

A graph grammar‐based approach for graph layout

As a two‐dimensional formal tool, graph grammars are capable of handling the layout problems of visual programming languages. Based on an edge‐based graph grammar (EGG), this paper proposes a novel layout approach that uses the unique features of EGG and overcomes the weakness of existing layout approaches. In order to make the approach rigorous yet concise, the graph grammar mechanisms with layout constraints and quantitative analysis techniques are combined together as an integrity. First, the basic notions of EGG are briefly introduced; second, the layout approach is presented that consists of two phases, ie, bottom‐up parsing and top‐down derivation. Finally, a case study is given by taking the standard flowchart as an example to demonstrate the working process of the proposed approach.     

String and graph grammar characterizations of bounded regular languages

Two grammatical characterizations of the bounded regular languages are presented: one in terms of graph grammars, the other using string grammars. First it is shown that a class of state graphs recognizing the bounded regular languages can be generated by a particular second-order contextfree graph grammar. Next we call uniquely recursive a right-linear (string) grammar having at most one right-recursive production for each of its nonterminals. It is then established that the class of languages generated by uniquely recursive, sequential right-linear grammars is exactly the bounded regular languages. Some comments on the relationship between string and graph grammars are made.     

A graph grammar programming style for recognition of music notation

Graph grammars are a promising tool for solving picture processing problems. However, the application of graph grammars to diagram recognition has been limited to rather simple analysis of local symbol configurations. This paper introduces the Build-Weed-Incorporate programming style for graph grammars and shows its application in determining the meaning of complex diagrams, where the interaction among physically distant symbols is semantically important. Diagram recognition can be divided into two stages: symbol recognition and high-level recognition. Symbol recognition has been studied extensively in the literature. In this work we assume the existence of a symbol recognizer and use a graph grammar to assemble the diagram's information content from the symbols and their spatial relationships. The Build-Weed-Incorporate approach is demonstrated by a detailed discussion of a graph grammar for high-level recognition of music notation. See Appendix A for an illustration of the terms for musical symbols used in this paper.     

Categorical approach to the construction of fuzzy graph grammars

The categorical approach is proposed to the formalization of fuzzy graph grammars obtained as a result of generalization of sequential graph grammars. This approach takes into consideration the basic types of fuzziness that arise in constructing categories of fuzzy objects and describing transformations of fuzzy graphs generated by fuzzy sets. All the problems of undecidability that are well known for Chomsky grammars are proved to hold true for fuzzy graph grammars. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 130–144, July–August 2006.