A comment on “Automata theory based on complete residuated lattice-valued logic: Pushdown automata”

Automata theory based on complete residuated lattice-valued logic has been first established by Qiu, and then has been systematically studied by Qiu and others. The definition of L -valued Chomsky Normal Form in Xing and Qiu [Automata theory based on complete residuated lattice-valued logic: pushdown automata, Fuzzy Sets and Systems 160 (2009) 1125–1140] is somewhat different from that in Xing and Qiu [Pumping lemma in context-free grammar theory based on complete residuated lattice-valued logic, Fuzzy Sets and Systems 160 (2009) 1141–1151]. In this note, we give a more general L -valued Chomsky Normal Form to unify the two definitions. We mainly show that, for an L -valued context-free grammar, an L -valued Greibach Normal Form can be equivalently constructed.