基于范畴论的形式语言模型建模方法研究  

ON FORMAL LANGUAGES MODELLING METHOD BASED ON CATEGORY THEORY

作　　者：苗德成[1] 奚建清[2] 苏锦钿[2] 

机构地区：[1]韶关学院数学与信息科学学院,广东韶关512005 [2]华南理工大学计算机科学与工程学院,广东广州510640

出　　处：《计算机应用与软件》2015年第4期19-23,共5页Computer Applications and Software

基　　金：国家自然科学基金项目(61103038);广东省自然科学基金项目(S2013010015944);广东省科技计划项目(2012A010701011;2012A010701003);韶关市科技局项目(2013CX/K61)

摘　　要：形式语言模型转换的语义一致性与其形式系统完备性分析是当前形式语言理论尚未有效解决的难题。针对形式语言模型的应用需求与研究现状,建立形式文法模型及其形式语言模型,应用范畴论方法构建具有普适意义的形式文法模型范畴与形式语言模型范畴。在形式语言族模型的形式化理论框架内,用与特定形式语言无关的范畴论方法研究形式语言模型转换的语义一致性。初步分析形式系统的完备性,通过与形式语言理论主要研究方法的比对论证了范畴论方法的优势,为形式语言模型的范畴论方法研究提供一个便利、高效的形式化理论框架。Semantic consistency of transformation of formal languages models and completeness analysis of formal system constituted by these formal languages models are the problems not being effectively solved yet in current formal languages theory.According to the application demands and research status of formal languages models,in this paper we build the formal grammar model and the formal languages model based on it,and construct the categories of formal grammar model and formal languages model with universality by using category theory.We also discuss the semantic consistency of transformation of formal languages models with category theory approach being independent of particular formal languages within the framework of formal languages family model,analyse preliminarily the completeness of formal system,and demonstrate the advantages of category theory approach by comparing it with some primary study methods of formal languages theory,which provides a convenient and efficient formal theory framework for studying the category theory approach of formal languages model.

关 键 词：模型 形式语言 范畴论 语义一致性 完备性 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]