CFG Parsing and Boolean Matrix Multiplication
نویسنده
چکیده
In this work the relation between Boolean Matrix Multiplication (BMM) and Context Free Grammar (CFG) parsing is shown. The first described approach, which is due to Valiant (1975), shows how CFG parsing can be reduced to Boolean Matrix Multiplication. Afterwards the reverse direction, i.e. how a CFG parser can be used to multiply two Boolean matrices, is presented, which is due to Lee (2002). The fundamental theorem that can be derived from the reductions is that fast CFG parsing requires fast Boolean matrix multiplication, and vice versa.
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