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.
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References
de Groote, P.: Towards abstract categorial grammars. In: Association for Computational Linguistics, 39th Annual Meeting and 10th Conference of the European Chapter, Proceedings of the Conference, pp. 148–155 (2001)
de Groote, P.: Tree-adjoining grammars as abstract categorial grammars. In: TAG+6, Proceedings of the 6th International Workshop on Tree Adjoining Grammars and Related Frameworks, Università di Venezia, pp. 145–150 (2002)
de Groote, P., Guillaume, B., Salvati, S.: Vector addition tree automata. In: Proceedings of the 19th Annual IEEE symposium on Logic in Computer Science, July 2004, pp. 64–73 (2004)
de Groote, P., Pogodalla, S.: m-linear context-free rewriting systems as abstract categorial grammars. In: Oehrle, R.T., Rogers, J. (eds.) Proceedings of Mathematics of Language - MOL-8, Bloomington, Indiana, U.S, June, pp. 71–80 (2003)
de Groote, P., Pogodalla, S.: On the expressive power of abstract categorial grammars: Representing context-free formalisms. Journal of Logic, Language and Information 13(4), 421–438 (2004)
Hopcroft, J.E., Pansiot, J.-J.: On the reachability problem for 5-dimensional vector addition systems. Theoretical Computer Science 8(2), 135–159 (1979)
Kanovich, M.I.: The complexity of Horn fragments of linear logic. Annals of Pure and Applied Logic 69, 195–241 (1994)
Kracht, M.: The Mathematics of Language. In: Studies in Generative Grammar, vol. 63, pp. 447–459. Mouton de Gruyter, Berlin (2003)
Lipton, R.J.: The reachability problem requires exponential space. Technical Report 62, Department of Computer Science, Yale University (January 1976)
Muskens, R.: Language, lambdas, and logic. In: Kruijff, G.-J., Oehrle, R. (eds.) Resource Sensitivity in Binding and Anaphora, Studies in Linguistics and Philosophy, pp. 23–54. Kluwer, Dordrecht (2003)
Rounds, W.C.: Complexity of recognition in intermediate-level languages. In: Proceedings of the 14th Annual IEEE Symposium on Switching and Automata Theory, October 1973, pp. 145–158 (1973)
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Yoshinaka, R., Kanazawa, M. (2005). The Complexity and Generative Capacity of Lexicalized Abstract Categorial Grammars. In: Blache, P., Stabler, E., Busquets, J., Moot, R. (eds) Logical Aspects of Computational Linguistics. LACL 2005. Lecture Notes in Computer Science(), vol 3492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11422532_22
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DOI: https://doi.org/10.1007/11422532_22
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