Advertisement

Minimalist Grammars with Unbounded Scrambling and Nondiscriminating Barriers Are NP-Hard

  • Alexander Perekrestenko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5196)

Abstract

Minimalist Grammars were proposed in [15] as a formalization of the basic structure-building component of the Minimalism Program, a syntactic framework introduced in [2] and [3]. In the present paper we investigate the effects of extending this formalism with an unrestricted scrambling operator together with nondiscriminating barriers. We show that the recognition problem for the resulting formalism NP-hard. The result presented here is a generalization of the result shown by the author in [14] for Minimalist Grammars with unrestricted scrambling and category-sensitive barriers.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Champollion, L.: Lexicalized non-local MCTAG with dominance links is NP-complete. In: Penn, G., Stabler, E. (eds.) Proceedings of Mathematics of Language 10. CSLI On-Line Publications UCLA (2007)Google Scholar
  2. 2.
    Chomsky, N.: The Minimalist Program. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  3. 3.
    Chomsky, N.: Derivation by phase. In: Kenstowicz, M. (ed.) Ken Hale: A Life in Language, pp. 1–52. MIT Press, Cambridge (2001)Google Scholar
  4. 4.
    de Groote, P., Morrill, G., Retoré, C. (eds.): LACL 2001. LNCS, vol. 2099. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  5. 5.
    Frey, W., Gärtner, H.: On the treatment of scrambling and adjunction in Minimalist Grammars. In: Jäger, G., Monachesi, P., Penn, G., Wintner, S. (eds.) Proceedings of the 7th Conference on Formal Grammar, pp. 41–52 (2002)Google Scholar
  6. 6.
    Gärtner, H., Michaelis, J.: Some remarks on locality conditions and Minimalist Grammars. In: Gärtner, H., Sauerland, U. (eds.) Interfaces + Recursion = Language? Chomsky’s Minimalism and the View from Syntax and Semantics, pp. 161–195. Walter de Gruyter, Berlin (2007)Google Scholar
  7. 7.
    Harkema, H.: A characterization of Minimalist languages. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, pp. 193–211. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Jäger, G., Monachesi, P., Penn, G., Wintner, S. (eds.): FG-MOL 2005: Proceedings of the 10th conference on Formal Grammar and the 9th Meeting on Mathematics of Language, Edinburgh, Scotland (2005)Google Scholar
  9. 9.
    Kobele, G., Michaelis, J.: Two type 0-variants of Minimalist Grammars. In: Jäger, et al. (eds.) [8]Google Scholar
  10. 10.
    Michaelis, J.: Derivational Minimalism is mildly context-sensitive. In: Moortgat, M. (ed.) LACL 1998. LNCS (LNAI), vol. 2014, pp. 179–198. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Michaelis, J.: Transforming linear context-free rewriting systems into Minimalist Grammars. In: de Groote, P., Morrill, G., Retoré, C. (eds.) LACL 2001. LNCS (LNAI), vol. 2099, pp. 228–244. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Michaelis, J.: An additional observation on strict derivational Minimalism. In: Jäger, et al. (eds.) [8]Google Scholar
  13. 13.
    Michaelis, J., Gärtner, H.: A note on countercyclicity and Minimalist Grammars. In: Jäger, G., Monachesi, P., Penn, G., Wintner, S. (eds.) Proceedings of the 8th Conference on Formal Grammar, pp. 103–114 (2003)Google Scholar
  14. 14.
    Perekrestenko, A.: A note on the complexity of the recognition problem for the Minimalist Grammars with unbounded scrambling and barriers. In: Madrigal, V.D., de Ros Salamanca, F.E. (eds.) Actas del XXIII Congreso de la Sociedad Española para el Procesamiento del Lenguaje Natural, Seville, Spain. Revista de la SEPLN, vol. 39, pp. 27–34 (2007)Google Scholar
  15. 15.
    Stabler, E.: Derivational Minimalism. In: Retoré, C. (ed.) LACL 1996. LNCS (LNAI), vol. 1328, pp. 68–95. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  16. 16.
    Søgaard, A., Lichte, T., Maier, W.: On the complexity of linguistically motivated extensions of tree-adjoining grammar. In: RANLP 2007: Proceedings of the Conference on Recent Advances in Natural Language Processing, Borovets, Bulgaria (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alexander Perekrestenko
    • 1
  1. 1.Research Group on Mathematical Linguistics International PhD School in Formal Languages and ApplicationsRovira i Virgili UniversityTarragonaSpain

Personalised recommendations