Constituent and dependency parsing, the two classic forms of syntactic parsing, have been found to benefit from joint training and decoding under a uniform formalism, Head-driven Phrase Structure Grammar (HPSG). However, decoding this unified grammar has a higher time complexity ($O(n^5)$) than decoding either form individually ($O(n^3)$) since more factors have to be considered during decoding. We thus propose an improved head scorer that helps achieve a novel performance-preserved parser in $O$($n^3$) time complexity. Furthermore, on the basis of this proposed practical HPSG parser, we investigated the strengths of HPSG-based parsing and explored the general method of training an HPSG-based parser from only a constituent or dependency annotations in a multilingual scenario. We thus present a more effective, more in-depth, and general work on HPSG parsing.
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