Weighted Multiple Context-Free Grammars

Abstract

Multiple context-free grammar (MCFG) is an extension of context-free grammar (CFG), which generates tuples of words. The expressive power of MCFG is between CFG and context-sensitive grammar while MCFG inherits good properties of CFG. In this paper, we introduce weighted multiple context-free grammar (WMCFG) as a quantitative extension of MCFG. Then we investigate properties of WMCFG such as polynomial-time computability of basic problems, its closure property and expressive power.