Automata theory based on complete residuated lattice-valued logic

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.