On multiple context-free grammars

Abstract

Multiple context-free grammars ( mcfg's) is a subclass of generalized context-free grammars introduced by Pollard (1984) in order to describe the syntax of natural languages. The class of languages generated by mcfg's (called multiple context-free languages or, shortly, mcfl's) properly includes the class of context-free languages and is properly included in the class of context-sensitive languages. First, the paper presents results on the generative capacity of mcfg's and also on the properties of mcfl's such as formal language-theoretic closure properties. Next, it is shown that the time complexity of the membership problem for multiple context-free languages is O( n e ), where n is the length of an input string and e is a constant called the degree of a given mcfg. Head grammars ( hg's) introduced by Pollard and tree adjoining grammars ( tag's) introduced by Joshi et al. (1975) are also grammatical formalisms to describe the syntax of natural languages. The paper also presents the following results on the generative capacities of hg's, tag's and 2-mcfg's, which are a subclass of mcfg's: (1) The class HL of languages generated by hg's is the same as the one generated by tag's; (2) HL is the same as the one generated by left-wrapping hg's (or right-wrapping hg's) which is a proper subclass of hg's; (3) HL is properly included in the one generated by 2-mcfg's. As a corollary of (1), it is also shown that HL is a substitution-closed full AFL.