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It reveals some equivalences between automata based on complete residuated lattice-valued logic (called e valued automata) and the truth-value lattice of the underlying logic (i.e. resid-uated lattice). In particular, it demonstrates several basic equivalent characterizations on the retriev-ability of e valued automata. Finally, the connections of the homomorphisms between two e valuedautomata to continuous mappings and open mappings are clarified. So this paper establishes furtherthe more profound fuzzy automata theory.