Fast context-free grammar parsing requires fast boolean matrix multiplication

In 1975, Valiant showed that Boolean matrix multiplication can be used for parsing contextfree 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(gn3), 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

• Type: Journal
• Year: 2002
• Where: JACM
• Authors: Lillian Lee
• Keywords: Boolean Matrix Multiplication, Cfg Parsers, JACM 2002, Parsing