Comparison with Other Algorithms

Abstract

There have been several general parsing algorithms that run in polynomial time. Theoretically speaking, the fastest algorithm at present is Valiant’s algorithm. Valiant [55] reduced the context-free parsing problem to the Boolean Matrix Multiplication problem [22], and his algorithm runs in time O(n^2.81). This algorithm is, however, of only theoretical interest, because the coefficient of n^2.81 is so large that the algorithm runs faster than conventional n³ algorithms only when an input sentence is tremendously long. Practically speaking, on the other hand, the most well-known parsing algorithm is Earley’s algorithm [21, 20, 1, 25], which runs in time O(n³). This book compares our algorithm mainly with this algorithm.