Pumping Lemma and Ogden Lemma for Displacement Context-Free Grammars

  • Alexey Sorokin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8633)


The pumping lemma and Ogden lemma offer a powerful method to prove that a particular language is not context-free. In 2008 Kanazawa proved an analogue of pumping lemma for well-nested multiple context-free languages. However, the statement of lemma is too weak for practical usage. We prove a stronger variant of pumping lemma and an analogue of Ogden lemma for this language family. We also use these statements to prove that some natural context-sensitive languages cannot be generated by tree-adjoining grammars.


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  1. 1.
    Joshi, A.K.: Tree adjoining grammars: How much context-sensitivity is required to provide reasonable structural descriptions? University of Pennsylvania, Moore School of Electrical Engineering, Department of Computer and Information Science (1985)Google Scholar
  2. 2.
    Joshi, A.K., Schabes, Y.: Tree-adjoining grammars. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 69–123. Springer (1997)Google Scholar
  3. 3.
    Kanazawa, M.: The pumping lemma for well-nested multiple context-free languages. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 312–325. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Kanazawa, M., Salvati, S.: MIX is not a tree-adjoining language. In: Proceedings of the 50th Annual Meeting of the Association for Computational Linguistics: Long Papers, vol. 1, pp. 666–674. Association for Computational Linguistics (2012)Google Scholar
  5. 5.
    Morrill, G., Valentín, O., Fadda, M.: The displacement calculus. Journal of Logic, Language and Information 20(1), 1–48 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Ogden, W.: A helpful result for proving inherent ambiguity. Theory of Computing Systems 2(3), 191–194 (1968)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Palis, M.A., Shende, S.M.: Pumping lemmas for the control language hierarchy. Mathematical Systems Theory 28(3), 199–213 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Pollard, C.: Generalized phrase structure grammars, head grammars, and natural languages. PhD thesis. Stanford University, Stanford (1984)Google Scholar
  9. 9.
    Seki, H., Matsumura, T., Fujii, M., Kasami, T.: On multiple context-free grammars. Theoretical Computer Science 88(2), 191–229 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Shieber, S.M.: Evidence against the context-freeness of natural language. In: The Formal Complexity of Natural Language, pp. 320–334. Springer (1987)Google Scholar
  11. 11.
    Sorokin, A.: Monoid automata for displacement context-free languages. In: ESSLLI Student Session 2013 Preproceedings, pp. 158–167 (2013),, Extended version to appear in ESSLLI Student Session 12-13 Selected Papers,
  12. 12.
    Sorokin, A.: Normal forms for multiple context-free languages and displacement Lambek grammars. In: Artemov, S., Nerode, A. (eds.) LFCS 2013. LNCS, vol. 7734, pp. 319–334. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  13. 13.
    Valentın, O., Morrill, G.: Theory of discontinuous Lambek calculus. PhD thesis. Universitat Autonoma de Barcelona (2012)Google Scholar
  14. 14.
    Vijay-Shanker, K., Weir, D.J., Joshi, A.K.: Tree adjoining and head wrapping. In: Proceedings of the 11th Conference on Computational Linguistics, pp. 202–207. Association for Computational Linguistics (1986)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexey Sorokin
    • 1
    • 2
  1. 1.Faculty of Mathematics and MechanicsMoscow State UniversityRussia
  2. 2.Faculty of Innovations and High TechnologiesMoscow Institute of Physics and TechnologyRussia

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