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}
}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…
139 Citations
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