We introduce a novel tagging scheme for discontinuous named entity recognition based on an explicit description of the inner structure of discontinuous mentions. We rely on a weighted finite state automaton for both marginal and maximum a posteriori inference. As such, our method is sound in the sense that (1) well-formedness of predicted tag sequences is ensured via the automaton structure and (2) there is an unambiguous mapping between well-formed sequences of tags and (discontinuous) mentions. We evaluate our approach on three English datasets in the biomedical domain, and report comparable results to state-of-the-art while having a way simpler and faster model.