Fast context-free grammar parsing requires fast boolean matrix multiplication

@article{Lee2002FastCG,
  title={Fast context-free grammar parsing requires fast boolean matrix multiplication},
  author={Lillian Lee},
  journal={J. ACM},
  year={2002},
  volume={49},
  pages={1-15}
}
  • Lillian Lee
  • Published 15 December 2001
  • Computer Science
  • J. ACM
In 1975, Valiant showed that Boolean matrix multiplication can be used for parsing context-free grammars (CFGs), yielding the asympotically fastest (although not practical) CFG parsing algorithm known. We prove a dual result: any CFG parser with time complexity <i>O</i>(<i>gn</i><sup>3-∈</sup>), where <i>g</i> is the size of the grammar and <i>n</i> is the length of the input string, can be efficiently converted into an algorithm to multiply <i>m</i> × <i>m</i> Boolean matrices in time <i>O</i… 

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