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Mathematical systems theory

, Volume 27, Issue 6, pp 511–546 | Cite as

The equivalence of four extensions of context-free grammars

  • K. Vijay-Shanker
  • D. J. Weir
Article

Abstract

There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms, namely, combinatory categorial grammars, head grammars, linear indexed grammars, and tree adjoining grammars. Each of these formalisms is known to generate a larger class of languages than context-free grammars. The four formalisms under consideration were developed independently and appear superficially to be quite different from one another. The result presented in this paper is that all four of the formalisms under consideration generate exactly the same class of string languages.

Keywords

Computational Mathematic Generative Power Large Class Computational Linguist Categorial Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A. V. Aho. Indexed grammars—an extension to context free grammars.J. Assoc. Comput. Mach.,15:647–671, 1968.Google Scholar
  2. [2]
    K. Ajdukiewicz. Die syntaktische Konnexität.Studia Philosophica,1:1–27, 1935. English translation in: S. McCall, editor,Polish Logic, 1920–1939, pp. 207–231. Oxford University Press, Oxford.Google Scholar
  3. [3]
    C. Culy. The complexity of the vocabulary of bambara.Ling. Philos.,8:345–351, 1985.Google Scholar
  4. [4]
    J. Duske and R. Parchmann. Linear indexed languages.Theoret. Comput. Sci.,32:47–60, 1984.Google Scholar
  5. [5]
    G. Gazdar. Applicability of indexed grammars to natural languages. In: U. Reyle and C. Rohrer, editors,Natural Language Parsing and Linguistic Theories, pp. 69–94. Reidel, Dordrecht, 1988.Google Scholar
  6. [6]
    G. Gazdar, E. Klein, G. K. Pullum, and I. A. Sag.Generalized Phrase Structure Grammars. Blackwell, Oxford, 1985. Also published by Harvard University Press, Cambridge, MA.Google Scholar
  7. [7]
    A. K. Joshi. How much context-sensitivity is necessary for characterizing structural descriptions —Tree Adjoining Grammars? In: D. Dowty, L. Karttunen, and A. Zwicky, editors,Natural Language Processing—Theoretical, Computational and Psychological Perspective, pp. 206–250. Cambridge University Press, New York, 1985. Originally presented in 1983.Google Scholar
  8. [8]
    A. K. Joshi, L. S. Levy, and M. Takahashi. Tree adjunct grammars.J. Comput. System Sci.,19(1):136–163, 1975.Google Scholar
  9. [9]
    T. Kasami. An efficient recognition and syntax algorithm for context-free languages. Technical Report AF-CRL-65-758, Air Force Cambridge Research Laboratory, Bedford, MA, 1965.Google Scholar
  10. [10]
    A. S. Kroch. Asymmetries in long distance extraction in a tag grammar. In: M. Baltin and A. S. Kroch, editors,New Conceptions of Phrase Structure, pp. 66–98. University of Chicago Press, Chicago, IL, 1986.Google Scholar
  11. [11]
    A. S. Kroch. Subjacency in a tree adjoining grammar. In: A. Manaster-Ramer, editor,Mathematics of Language, pp. 143–172. Benjamins, Amsterdam, 1987.Google Scholar
  12. [12]
    A. S. Kroch and A. K. Joshi. Linguistic relevance of tree adjoining grammars. Technical Report MS-CIS-85-18, Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, 1985.Google Scholar
  13. [13]
    A. S. Kroch and A. K. Joshi. Analyzing extraposition in a tree adjoining grammar. In: G. Huck and A. Ojeda, editors,Syntax and Semantics: Discontinuous Constituents, pp. 107–149. Academic Press, New York, 1986.Google Scholar
  14. [14]
    A. S. Kroch and B. Santorini. The derived constituent structure of West Germanic verb-raising construction. In: R. Freiden, editor,Proceedings of the Princeton Workshop on Grammar, pp. 269–338, 1991.Google Scholar
  15. [15]
    C. Pollard. Generalized Phrase Structure Grammars, Head Grammars, and Natural Language. Ph.D. thesis, Stanford University, CA, 1984.Google Scholar
  16. [16]
    G. Pullum and G. Gazdar. Natural languages and context-free languages.Ling. Philos.,4:471–504, 1982.Google Scholar
  17. [17]
    K. Roach. Formal properties of head grammars. In: A. Manaster-Ramer, editor,Mathematics of Language, pp. 293–348. Benjamins, Amsterdam, 1987.Google Scholar
  18. [18]
    B. Santorini. The West Germanic verb-raising construction: a tree adjoing grammar analysis. Master's thesis, University of Pennsylvania, Philadelphia, PA, 1986.Google Scholar
  19. [19]
    S. M. Shieber. Evidence against the context-freeness of natural language.Ling. Philos.,8:333–343, 1985.Google Scholar
  20. [20]
    M. J. Steedman. Dependency and coordination in the grammar of Dutch and English.Language,61:523–568, 1985.Google Scholar
  21. [21]
    M. J. Steedman. Combinators and grammars. In: R. Oehrle, E. Bach, and D. Wheeler, editors,Categorial Grammars and Natural Language Structures, pp. 417–442. Foris, Dordrecht, 1986.Google Scholar
  22. [22]
    K. Vijay-Shanker. A study of tree adjoining grammars. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA, 1987.Google Scholar
  23. [23]
    K. Vijay-Shanker and D. J. Weir. Parsing constrained grammar formalisms.Comput. Linguistics, to appear.Google Scholar
  24. [24]
    K. Vijay-Shanker and D. J. Weir. Polynomial parsing of extensions of context-free grammars. In: M. Tomita, editor,Current Issues in Parsing Technology, pp. 191–206. Kluwer, Boston, 1991.Google Scholar
  25. [25]
    K. Vijay-Shanker, D. J. Weir, and A. K. Joshi. Tree adjoining and head wrapping.Proceedings of the 11th International Conference on Computational Linguistics, pp. 202–207, 1986.Google Scholar
  26. [26]
    D. J. Weir. Characterizing mildly context-sensitive grammar formalisms. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA, 1988.Google Scholar
  27. [27]
    D. J. Weir. A geometric hierarchy beyond context-free languages.Theoret. Comput. Sci.,104:235–261, 1992.Google Scholar
  28. [28]
    D. J. Weir and A. K. Joshi. Combinatory categorial grammars: generative power and relationship to linear context-free rewriting systems.Proceedings of the 26th Meeting of the Association on Computational Linguistics, pp. 278–285, 1988.Google Scholar
  29. [29]
    D. H. Younger. Recognition and parsing of context-free languages in timen 3.Inform. and Control,10(2):189–208, 1967.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • K. Vijay-Shanker
    • 1
  • D. J. Weir
    • 2
  1. 1.Department of Computer and Information ScienceUniversity of DelawareNewarkUSA
  2. 2.School of Cognitive and Computing SciencesUniversity of SussexBrightonEngland

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