AbstractThis paper considers the task of parsing low-resource languages in a scenario where parallel English data and also a limited seed of annotated sentences in the target language are available, as for example in bootstrapping parallel treebanks. We focus on constituency parsing using Role and Reference Grammar (RRG), a theory that has so far been understudied in computational linguistics but that is widely used in typological research, i.e., in particular in the context of low-resource languages. Starting from an existing RRG parser, we propose two strategies for low-resource parsing: first, we extend the parsing model into a cross-lingual parser, exploiting the parallel data in the high-resource language and unsupervised word alignments by providing internal states of the source-language parser to the target-language parser. Second, we adopt self-training, thereby iteratively expanding the training data, starting from the seed, by including the most confident new parses in each round. Both in simulated scenarios and with a real low-resource language (Daakaka), we find substantial and complementary improvements from both self-training and cross-lingual parsing. Moreover, we also experimented with using gloss embeddings in addition to token embeddings in the target language, and this also improves results. Finally, starting from what we have for Daakaka, we also consider parsing a related language (Dalkalaen) where glosses and English translations are available but no annotated trees at all, i.e., a no-resource scenario wrt. syntactic annotations. We start with cross-lingual parser trained on Daakaka with glosses and use self-training to adapt it to Dalkalaen. The results are surprisingly good.