Fast uniform analysis of Coupled-Context-Free languages

Abstract

Coupled-Context-Free Grammars are a natural generalization of context-free grammars obtained by combining nonterminals to corresponding parentheses which can only be substituted simultaneously. Refering to the generative capacity we obtain an infinite hierarchy of languages that comprises the context-free languages as the first and 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 from one subclass to the next powerful one by the factor of the squared input length. For all our grammars, this complexity is only linear in its size which is dominating in the case of the large grammars for natural languages, where the sentences are short.KeywordsNormal FormTime ComplexityDerivation TreeInfinite LoopProduction NodeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.