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The notion of latent-variable probabilistic context-free derivation of syntactic structures is enhanced to allow heads and unrestricted discontinuities. The chosen formalization covers both constituency parsing and dependency parsing. By the new framework, one obtains a probability distribution over the space of all discontinuous parses. This lends itself to intrinsic evaluation in terms of cross-entropy. The derivational model is accompanied by an equivalent automaton model, which can be used for deterministic parsing.
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