LR(K)-COUPLED-CONTEXT-FREE GRAMMARS

Coupled-context-free grammars are a generalization of context-free grammars obtained by combining nonterminals to parentheses which can only be substituted simultaneously. Referring to the generative capacity of the grammars which grows with the number of nonterminals allowed to be substituted simultaneously, we obtain an infinite hierarchy of language classes. The smallest class in this hierarchy are the context-free languages, the second smallest class are all the languages generated by Tree Adjoining Grammars (TAGs) (at most two nonterminals are replaced simultaneously). The latter is important because today, TAGs are commonly used to model the syntax of natural languages. Here, we present a generalization of the context-free LR(k)-notion, which characterizes for each language class in the hierarchy generated by coupled-context-free grammars - and therefore for TAGs, too - a subclass, which can be parsed in linear time. The parsing algorithm described maintains the Valid Prefix Property and the incremental procedure of the context-free prototype. Thus, it can be used for on-line parsing of natural language. It is illustrated by examples that important Tree Adjoining Languages, e.g. those modelling cross-serial dependencies, can be generated by LR(k) -coupled-context-free grammars.