计算机工程与应用 ›› 2012, Vol. 48 ›› Issue (28): 57-60.

• 研究、探讨 • 上一篇    下一篇

基于Unsharp量子逻辑的自动机和文法理论

彭家寅   

  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
  • 出版日期:2012-10-01 发布日期:2012-09-29

Automata and grammars theory based on Unsharp quantum logic

PENG Jiayin   

  1. Key Laboratory of Numerical Simulation of Sichuan Provice, School of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, China
  • Online:2012-10-01 Published:2012-09-29

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。

关键词: unsharp量子逻辑, &epsilon, -值自动机&epsilon, -值正则文法, &epsilon, -值正则语言, 正则算子

Abstract: A fundamental framework of automata and grammar theory based on the two unsharp quantum structures, 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 any ε-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, concatenation and reversal are respectively discussed.

Key words: unsharp quantum logic, ε-valued automaton, ε-valued regular grammar, ε-valued regular language, regular operation