Access Restriction

Author Lee, Lillian
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2002
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Boolean matrix multiplication ♦ Context-free grammar parsing
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 $O(gn^{3-∈}),$ where $\textit{g}$ is the size of the grammar and $\textit{n}$ is the length of the input string, can be efficiently converted into an algorithm to multiply $\textit{m}$ × $\textit{m}$ Boolean matrices in time $O(m^{3-∈/3}).$ Given that practical, substantially subcubic Boolean matrix multiplication algorithms have been quite difficult to find, we thus explain why there has been little progress in developing practical, substantially subcubic general CFG parsers. In proving this result, we also develop a formalization of the notion of parsing.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2002-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 49
Issue Number 1
Page Count 15
Starting Page 1
Ending Page 15

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Source: ACM Digital Library