Automata theory based on complete residuated lattice-valued logic: Pushdown automata

Automata theory based on complete residuated lattice-valued logic, called L-valued automata, has been proposed by Qiu [Automata theory based on complete residuated latticed-valued logic, Sci. China (Ser. F) 44 (6) (2001) 419–429; Automata theory based on complete residuated latticed-valued logic (II), Sci. China (Ser. F) 45 (6) (2002) 442–452]. In this paper, we discuss some properties of L-valued context-free grammars, languages, and pushdown automata. We show that, for such grammars, Chomsky and Greibach Normal Forms can be equivalently constructed, and we also prove that the languages accepted by final states and by empty stack in L-valued pushdown automata are equivalent. In particular, we prove the equivalence between L-valued context-free grammars and L-valued pushdown automata.