A Fast Algorithm for Computing Prefix Probabilities

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(n3 |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(n2 |N|3+n3|N|2).