An O(n^3) Agenda-Based Chart Parser for Arbitrary Probabilistic Context-Free Grammars

While $O(n^3)$ methods for parsing probabilistic context-free grammars (PCFGs) are well known, a tabular parsing framework for arbitrary PCFGs which naturally allows top-down, bottom-up, and other strategies, corresponding to active chart parsing for CFGs, has not yet been provided. This paper presents such an algorithm, and shows its correctness and advantages over prior work. The paper finishes by bringing out the connections between the algorithm and work on hypergraphs, which permits us to extend the presented Viterbi (best parse) algorithm to an inside (total probability) algorithm.

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