The complexity and generative capacity of lexicalized abstract categorial grammars

Authors:
Ryo Yoshinaka;Makoto Kanazawa
Affiliations:
National Institute of Informatics, Tokyo, Japan;National Institute of Informatics, Tokyo, Japan
Venue:
LACL'05 Proceedings of the 5th international conference on Logical Aspects of Computational Linguistics
Year:
2005

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Abstract

Previous studies have shown that some well-known classes of grammars can be simulated by Abstract Categorial Grammars (de Groote 2001) in straightforward ways. These classes of grammars all generate subclasses of the PTIME languages. While the exact generative capacity of the class of ACGs and the complexity of its universal membership problem are both unknown, we show that the universal membership problem for the class of lexicalized ACGs is NP-complete and the languages generated by lexicalized ACGs form a subclass of NP which includes some NP-complete languages.