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