Article ID Journal Published Year Pages File Type
390207 Fuzzy Sets and Systems 2009 11 Pages PDF
Abstract

Residuated lattices are important algebras and have close links with various important algebras. Automata theory based on complete residuated lattice-valued logic, called L-valued automata, has been established by the second author in 2001 and 2002. As a continuation of automata theory based on complete residuated lattice-valued logic, in this paper, we mainly deal with the problem concerning pumping lemma in L-valued context-free languages (L-CFLs). As a generalization of the notion in the theory of formal grammars, the definition of L-valued context-free grammars (L-CFGs) is introduced. We also discuss a special case of L-CFGs, L-right (or left)-linear grammars, and show the equivalence between L-linear grammars and L-regular grammars. This result shows that we generalize the pumping lemma in L-valued regular languages (L-RLs) more recently established by the second author.

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