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两类非经典有限自动机的性质与乘积研究

更新时间 2009-11-11 12:27:26 点击数:

两类非经典有限自动机的性质与乘积研究
Research on Characterizations and Products of Two Kinds of Nonclassical Finite Automata
【中文摘要】 本文研究了Mealy-型模糊有限自动机的乘积和基于量子逻辑自动机的可达和可识性质.全文共四章,具体内容如下:在第一章中,介绍一些记号及基本定义和性质.在第二章中,我们引进了Mealy-型模糊有限自动机乘积的几种构造方式,以及覆盖概念,讨论了此类型自动机的转移函数和输出函数的性质.进而,研究了这些自动机及乘积间的相互覆盖关系.最后,证明了一些覆盖关系在商自动机的乘积间也成立.在第三章中,我们在经典自动机和量子逻辑自动机理论基础上,定义了量子有限自动机的可逆,可达,余可达,完备概念;讨论了这些概念的相关性质.并且使用语义分析的方法证明了在量子逻辑框架下这些类型自动机的可识和可达性质.在第四章中,总结全文,并提出了一些待解决的问题.这些重要而有兴趣的问题将是我们未来研究工作的方向.

【英文摘要】 This thesis is concerned with products of Mealy-type fuzzy fi-nite automata, and recognizability and accessibility of finite automata based onquantum logic. This thesis is divided into four chapters. It is organized as follows:In Chapter 1, we introduce some marks and basic definitions.In Chapter 2, we introduce several ways of constructing products for Mealy-type fuzzy finite automata as well as the concept of covering. The propertiesof transition functions and output functions are discussed. Furthermore, we in-vestigate the covering properties and mutual relationship with regard to theseproducts. We also prove that the covering relationship holds in the product offactor automata.In Chapter 3, inspired by classical automata theory and automata theorybased on quantum logic, we introduce the concepts of reversal, accessible, coac-cessible and complete part of finite state automata based on quantum logic. Someproperties of them are discussed. More importantly we investigate the recogniz- http://www.lwfor.com ability and accessibility properties of these types on the framework of quantumlogic by employing the approach of semantic analysis.In Chapter 4, we conclude this thesis and list some problems which areneeded to solve. These problems are much more interesting and important workto be done in the future.

【中文关键词】 Mealy-模糊有限自动机; 级联积; 圈积; 直积; 量子逻辑; 量子有限自动机
【英文关键词】 Mealy-fuzzy finite automata; cascade product; wreath product; direct product; direct product; quantum logic; quantum finite automata
  两类非经典有限自动机的性质与乘积研究

摘要 3-4
Abstract 4
引言 6-11
第一章 预备知识 11-13
    1.1 模糊集合理论基础 11
    1.2 有限状态自动机 11-12
    1.3 模糊有限状态自动机 12-13
第二章 Mealy-型模糊有限自动机的乘积 13-30
    2.1 基础知识 13-15
    2.2 Mealy-型模糊有限自动机乘积的定义及性质 15-21
    2.3 圈积和级联积的分离性质 21-23
    2.4 自动机及其乘积间的覆盖关系 23-29
    2.5 本章小结 29-30
第三章 基于量子逻辑的自动机理论: 可识和可达 30-42
    3.1 基础知识 30-32
    3.2 l-值可逆自动机 32-34
    3.3 l-值可达自动机 34-38
    3.4 l-值完备自动机 38-41
    3.5 本章小结 41-42
第四章 总结与展望 42-44
参考文献 44-48
致谢 48-49
攻读硕士学位期间的科研成果 49

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