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Abstract: 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 $O(g n^{3 - \epsilson})$, where $g$ is the size of the grammar and $n$ is the length of the input string, can be efficiently converted into an algorithm to multiply $m \times m$ Boolean matrices in time $O(m^{3 - \epsilon/3})$. Given... (Update)
Context of citations to this paper: More
.... context free grammars [3, 20] Since nondeterministic parsing is equivalent in computational complexity to boolean matrix multiplication [12], a linear time solution to this more general problem is unlikely to be found. 5.2 Stateless Parsing A second limitation of packrat...
...much harder problem than recognizing regular expressions. Parsing arbitrary CFGs is equivalent in complexity to boolean matrix multiplication [13], which is generally believed to lie between O(n ) and O(n ) The fastest known algorithm to recognize arbitrary unambiguous CFGs is...
Cited by: More
Parsing Expression Grammars: A Recognition-Based Syntactic.. - Ford (2004) (Correct)
Packrat Parsing: a Practical Linear-Time Algorithm with Backtracking - Ford (2002) (Correct)
Packrat Parsing: Simple, Powerful, Lazy, Linear Time - Ford (Correct)
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BibTeX entry: (Update)
Lillian Lee. Fast context-free grammar parsing requires fast boolean matrix multiplication. Journal of the ACM, 2002. To appear. http://citeseer.ist.psu.edu/lee02fast.html More
@article{ lee02fast,
author = "Lillian Lee",
title = "Fast context-free grammar parsing requires fast boolean matrix multiplication",
journal = "Journal of the ACM",
volume = "49",
number = "1",
pages = "1-15",
year = "2002",
url = "citeseer.ist.psu.edu/lee02fast.html" }
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