Fast context-free parsing requires fast Boolean matrix multiplication
conference of the european chapter of the association for computational linguistics（1997）
摘要
Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time O(|G||w|3-e) on a grammar G and a string w can be used to multiply m x m Boolean matrices in tmie O(m3-e/3). In the process we also provide a formal definition of parsing motivated by an informal notion due to Lang. Our result establishes one of the first limitations on general CFG parsing: a fast, practical CFG parser would yield a fast, practical BMM algorithm, which is not believed to exist.
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关键词
boolean matrix multiplication,time o,cfg parsing,context-free parsing,general cfg parsing,formal definition,practical bmm algorithm,practical cfg parser,grammar g,informal notion,dual result,matrix multiplication
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