  This work revisits the topic of jointly parsing constituency and dependency
trees, i.e., to produce compatible constituency and dependency trees
simultaneously for input sentences, which is attractive considering that the
two types of trees are complementary in representing syntax. The original work
of Zhou and Zhao (2019) performs joint parsing only at the inference phase.
They train two separate parsers under the multi-task learning framework (i.e.,
one shared encoder and two independent decoders). They design an ad-hoc dynamic
programming-based decoding algorithm of $O(n^5)$ time complexity for finding
optimal compatible tree pairs. Compared to their work, we make progress in
three aspects: (1) adopting a much more efficient decoding algorithm of
$O(n^4)$ time complexity, (2) exploring joint modeling at the training phase,
instead of only at the inference phase, (3) proposing high-order scoring
components to promote constituent-dependency interaction. We conduct
experiments and analysis on seven languages, covering both rich-resource and
low-resource scenarios. Results and analysis show that joint modeling leads to
a modest overall performance boost over separate modeling, but substantially
improves the complete matching ratio of whole trees, thanks to the explicit
modeling of tree compatibility.
