基于Unsharp量子逻辑的自动机和文法理论  

Automata and grammars theory based on Unsharp quantum logic

作　　者：彭家寅[1] 

机构地区：[1]四川省高等学校数值仿真重点实验室,内江师范学院数学与信息科学学院,四川内江641112

出　　处：《计算机工程与应用》2012年第28期57-60,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11071178);四川省科技厅重点科技项目(No.2006J13-035);四川省教育厅重点实验室专项(No.2006ZD050)

摘　　要：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。A fundamental framework of automata and grammar theory based on the two unsharp quantum struc- tures, extended lattice ordered effect algebra and lattice ordered QMV algebra with a certain kind of distributive law, is preliminarily established in this paper. The concept of ε -valued regular grammar is introduced. It is showed that any ε -valued language recognized by ε -valued automaton is equivalent to that generated by some ε-valued regular grammar, the ε-valued language generated by anyε -valued regular grammar is also equivalent to that recognized by some ε-valued automaton. The closure properties of ε -valued language under the operations of sum, concatena- tion and reversal are respectively discussed.

关 键 词：unsharp量子逻辑 ε-值自动机 ε-值正则文法 ε-值正则语言 正则算子 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]