Closure Properties of Minimalist Derivation Tree Languages

  • Thomas Graf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6736)


Recently, the question has been raised whether the derivation tree languages of Minimalist grammars (MGs; [14, 16]) are closed under intersection with regular tree languages [4, 5]. Using a variation of a proof technique devised by Thatcher [17], I show that even though closure under intersection does not obtain, it holds for every MG and regular tree language that their intersection is identical to the derivation tree language of some MG modulo category labels. It immediately follows that the same closure property holds with respect to union, relative complement, and certain kinds of linear transductions. Moreover, enriching MGs with the ability to put regular constraints on the shape of their derivation trees does not increase the formalism’s weak generative capacity. This makes it straightforward to implement numerous linguistically motivated constraints on the Move operation.


Minimalist Grammars Derivation Tree Languages Closure Properties Regular Tree Languages Derivational Constraints 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chomsky, N.: The Minimalist Program. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  2. 2.
    Chomsky, N.: Derivation by phase. In: Kenstowicz, M.J. (ed.) Ken Hale: A Life in Language, pp. 1–52. MIT Press, Cambridge (2001)Google Scholar
  3. 3.
    Gärtner, H.M., Michaelis, J.: Some remarks on locality conditions and minimalist grammars. In: Sauerland, U., Gärtner, H.M. (eds.) Interfaces + Recursion = Language? Chomsky’s Minimalism and the View from Syntax-Semantics, pp. 161–196. Mouton de Gruyter, Berlin (2007)Google Scholar
  4. 4.
    Graf, T.: Reference-set constraints as linear tree transductions via controlled optimality systems. In: Proceedings of the 15th Conference on Formal Grammar (2010) (to appear)Google Scholar
  5. 5.
    Graf, T.: A tree transducer model of reference-set computation. UCLA Working Papers in Linguistics 15, article 4 (2010)Google Scholar
  6. 6.
    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
  7. 7.
    Joshi, A.: Tree-adjoining grammars: How much context sensitivity is required to provide reasonable structural descriptions? In: Dowty, D., Karttunen, L., Zwicky, A. (eds.) Natural Language Parsing, pp. 206–250. Cambridge University Press, Cambridge (1985)CrossRefGoogle Scholar
  8. 8.
    Kobele, G.M.: Features moving madly: A formal perspective on feature percolation in the minimalist program. Research on Language and Computation 3(4), 391–410 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kobele, G.M.: Generating Copies: An Investigation into Structural Identity in Language and Grammar. Ph.D. thesis, UCLA (2006)Google Scholar
  10. 10.
    Kobele, G.M., Retoré, C., Salvati, S.: An Automata-Theoretic Approach to Minimalism. In: Rogers, J., Kepser, S. (eds.) Model Theoretic Syntax at 10, pp. 71–80 (2007)Google Scholar
  11. 11.
    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
  12. 12.
    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
  13. 13.
    Rogers, J.: A Descriptive Approach to Language-Theoretic Complexity. CSLI, Stanford (1998)zbMATHGoogle Scholar
  14. 14.
    Stabler, E.P.: Derivational minimalism. In: Retoré, C. (ed.) LACL 1996. LNCS (LNAI), vol. 1328, pp. 68–95. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  15. 15.
    Stabler, E.P.: Computational perspectives on minimalism. In: Boeckx, C. (ed.) Oxford Handbook of Linguistic Minimalism, pp. 617–643. Oxford University Press, Oxford (2011)Google Scholar
  16. 16.
    Stabler, E.P., Keenan, E.: Structural similarity. Theoretical Computer Science 293, 345–363 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Thatcher, J.W.: Characterizing derivation trees for context-free grammars through a generalization of finite automata theory. Journal of Computer and System Sciences 1, 317–322 (1967)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Thomas Graf
    • 1
  1. 1.Department of LinguisticsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations