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Shi, Huang, and Lee (2017) obtained state-of-the-art results for English and Chinese dependency parsing by combining dynamic-programming implementations of transition-based dependency parsers with a minimal set of bidirectional LSTM features. However, their results were limited to projective parsing. In this paper, we extend their approach to support non-projectivity by providing the first practical implementation of the MH4 algorithm, an O(n^4) mildly nonprojective dynamic-programming parser with very high coverage on non-projective treebanks. To make MH4 compatible with minimal transition-based feature sets, we introduce a transition-based interpretation of it in which parser items are mapped to sequences of transitions. We thus obtain the first implementation of global decoding for non-projective transition-based parsing, and demonstrate empirically that it is more effective than its projective counterpart in parsing a number of highly non-projective languages. 

We generalize Cohen, Gómez-Rodríguez, and Satta’s (2011) parser to a family of non-projective transition-based dependency parsers allowing polynomial-time exact inference. This includes novel parsers with better coverage than Cohen et al. (2011), and even a variant that reduces time complexity to O(n^6), improving on prior bounds. We hope that this piece of theoretical work inspires design of novel transition systems with better coverage and better run-time guarantees.