Automata theory based on complete residuated lattice-valued logic  

作　　者：邱道文 

出　　处：《Science in China(Series F)》2001年第6期419-429,共11页中国科学（F辑英文版）

基　　金：This work was supported by the National Foundation for Distinguished Young Scholars (Grant No. 69725004); the National Key Project for Basic Research (Grant No.1998030509) ; the National Natural Science Foundation of China (Grant No. 69823001).

摘　　要：This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a characterization of residuated lattice by fuzzy automata (called (?) valued automata). After that fuzzy subautomata (called (?) valued subautomata), successor and source operators are pro-posed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally an L bifuzzy topological characterization of Q valued automata is presented, so a more generalized fuzzy automata theory is built.This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a characterization of residuated lattice by fuzzy automata (called (?) valued automata). After that fuzzy subautomata (called (?) valued subautomata), successor and source operators are pro-posed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally an L bifuzzy topological characterization of Q valued automata is presented, so a more generalized fuzzy automata theory is built.

关 键 词：non-classical logics AUTOMATA topology. 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]