We formulate a generalization of Petrov et al. (2006)’s split/merge algorithm for interpreted regular tree grammars (Koller and Kuhlmann, 2011), which capture a large class of grammar formalisms. We evaluate its effectiveness empirically on the task of discontinuous constituent parsing with two mildly context-sensitive grammar formalisms: linear context-free rewriting systems (Vijay-Shanker et al., 1987) as well as hybrid grammars (Nederhof and Vogler, 2014).

We explore the concept of hybrid grammars, which formalize and generalize a range of existing frameworks for dealing with discontinuous syntactic structures. Covered are both discontinuous phrase structures and non-projective dependency structures. Technically, hybrid grammars are related to synchronous grammars, where one grammar component generates linear structures and another generates hierarchical structures. By coupling lexical elements of both components together, discontinuous structures result. Several types of hybrid grammars are characterized. We also discuss grammar induction from treebanks. The main advantage over existing frameworks is the ability of hybrid grammars to separate discontinuity of the desired structures from time complexity of parsing. This permits exploration of a large variety of parsing algorithms for discontinuous structures, with different properties. This is confirmed by the reported experimental results, which show a wide variety of running time, accuracy, and frequency of parse failures.