On parsing coupled-context-free languages

Abstract

Coupled-Context-Free Grammars are a natural generalization of context-free grammars obtained by combining nonterminals to parentheses which can only be substituted simultaneously. Refering to the generative capacity of the grammars we obtain an infinite hierarchy of languages that comprises the context-free languages as the first and all the languages generated by Tree Adjoining Grammars (TAGs) as the second element. The latter is important because today, TAGs are commonly used to model the syntax of natural languages. Here, we present an approach to analyse all language classes of the hierarchy uniformly. The distinct generative capacity of the subclasses is reflected in the time complexity of the algorithm which grows by the factor of the squared input length from one subclass to the next powerful one. For all our grammars, this complexity is only linear in its size which is dominating in case of the large grammars for natural languages, where the sentences are usually short. In addition, we show how to generate the normal form required by our algorithm and discuss subclasses which can be analysed faster than the general case.