@inproceedings{nowak-cotterell-2023-fast,
    title = "A Fast Algorithm for Computing Prefix Probabilities",
    author = "Nowak, Franz  and
      Cotterell, Ryan",
    editor = "Rogers, Anna  and
      Boyd-Graber, Jordan  and
      Okazaki, Naoaki",
    booktitle = "Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)",
    month = jul,
    year = "2023",
    address = "Toronto, Canada",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2023.acl-short.6",
    doi = "10.18653/v1/2023.acl-short.6",
    pages = "57--69",
    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 new speed-up of Jelinek and Lafferty{'}s (1991) algorithm, which runs in $O(n^3|N|^3 + |N|^4)$, where n is the input length and |N| is the number of non-terminals in the grammar. In contrast, our speed-up runs in $O(n^2|N|^3 + n^3|N|^2)$.",
}

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 new speed-up of Jelinek and Lafferty{'}s (1991) algorithm, which runs in $O(n^3|N|^3 + |N|^4)$, where n is the input length and |N| is the number of non-terminals in the grammar. In contrast, our speed-up runs in $O(n^2|N|^3 + n^3|N|^2)$.
Nowak, Franz Cotterell, Ryan
A Fast Algorithm for Computing Prefix Probabilities