Abstract A fundamental framework of automata and grammars theory based on complete residuated lattice-valued logic is preliminarily established. Firstly, the concept of l value regular grammars is introduced. It is proved that any l value language recognized by l value automaton is equivalent to that generated by some l value regular grammar, and conversely, the l value language generated by any l value regular grammar is also equivalent to that recognized by some l value automaton. Afterwards, the concatenations of l value automaton and l value language recognized by l value automaton are depicted. In particular, the l value pumping lemma and L value pumping lemma are built, and then a decision characterization of l value language is presented. Finally, the equivalence between the l value automata with ε-transitions and those without ε-transitions is revealed.
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