A Fast Algorithm for Computing Prefix Probabilities

Abstract

Multiple algorithms are known for efficiently calculating the prefix probability of a string under a probabilistic context-free grammar (PCFG). Good algorithms for the problem have a runtime cubic in the length of the input string. However, some proposed algorithms are suboptimal with respect to the size of the grammar. This paper proposes a novel speed-up of Jelinek and Lafferty's (1991) algorithm, whose original runtime is $O(n^3|N{|}^3+|N{|}^4)$, where $n$ is the input length and $|N|$ is the number of non-terminals in the grammar. In contrast, our speed-up runs in $O(n^2|N{|}^3+n^3|N{|}^2)$.

Corrected typos, changed the layout of the algorithms, and improved appendix B on the semiring version of the algorithm