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

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