Syntactic dependency structures are based on the assumption that there is exactly one node in the structure for each word in the sentence. However representing elliptical constructions (e.g. missing verbs) is problematic as the question where the dependents of the elided material should be attached to has to be solved. In this paper, we present an in-depth study into the challenges of introducing empty heads into dependency structures during automatic parsing. Structurally, empty heads provide an attachment site for the dependents of the non-overt material and thus preserve the linguistically plausible structure of the sentence. We compare three different (computational) approaches to the introduction of empty heads and evaluate them against German and Hungarian data. We then conduct a fine-grained error analysis on the output of one of the approaches to highlight some of the difficulties of the task. We find that while a clearly defined part of the phenomena can be learned by the parser, more involved elliptical structures are still mostly out of reach of the automatic tools.
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