Skip to main content

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

  • Conference paper
Book cover Language and Automata Theory and Applications (LATA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This research work has been supported by the Russian Foundation for the Humanities as a part of the project “The typology of free word order languages” (grant RGNF 06-04-00203a).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Chomsky, N.: The Minimalist Program. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  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. de Groote, P., Morrill, G., Retoré, C. (eds.): LACL 2001. LNCS, vol. 2099. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  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. Kobele, G., Michaelis, J.: Two type 0-variants of Minimalist Grammars. In: Jäger, et al. (eds.) [8]

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  12. Michaelis, J.: An additional observation on strict derivational Minimalism. In: Jäger, et al. (eds.) [8]

    Google Scholar 

  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. 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. Stabler, E.: Derivational Minimalism. In: Retoré, C. (ed.) LACL 1996. LNCS (LNAI), vol. 1328, pp. 68–95. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Perekrestenko, A. (2008). Minimalist Grammars with Unbounded Scrambling and Nondiscriminating Barriers Are NP-Hard. In: Martín-Vide, C., Otto, F., Fernau, H. (eds) Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science, vol 5196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88282-4_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88282-4_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88281-7

  • Online ISBN: 978-3-540-88282-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics