Mathematical systems theory

, Volume 27, Issue 6, pp 511–546

The equivalence of four extensions of context-free grammars

  • K. Vijay-Shanker
  • D. J. Weir

DOI: 10.1007/BF01191624

Cite this article as:
Vijay-Shanker, K. & Weir, D.J. Math. Systems Theory (1994) 27: 511. doi:10.1007/BF01191624


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.

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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