We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.

Constituent parsing has been studied extensively in the last decades. Chomsky-Schützenberger parsing as an approach to constituent parsing has only been investigated theoretically, yet. It uses the decomposition of a language into a regular language, a homomorphism, and a bracket language to divide the parsing problem into simpler subproblems. We provide the first implementation of Chomsky-Schützenberger parsing. It employs multiple context-free grammars and incorporates many refinements to achieve feasibility. We compare its performance to state-of-the-art grammar-based parsers.

We prove a Chomsky-Schützenberger representation theorem for multiple context-free languages weighted over complete commutative strong bimonoids. Using this representation we devise a parsing algorithm for a restricted form of those devices.

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We use a non-deterministic variant of storage types to develop a framework for the approximation of automata with storage. This framework is used to provide automata-theoretic views on the approximation of multiple context-free languages and on coarse-to-fine parsing.