BIT Numerical Mathematics

, Volume 22, Issue 1, pp 17–26 | Cite as

A new proof technique to establish equivalence of the original and the generatedλ-free CFG with linear increase in size

  • Jainendra Navlakha
Part I Computer Science
  • 23 Downloads

Abstract

To generate an equivalentλ-free context free grammar from an arbitrary CFG, the most efficient algorithms described in the literature increase the size of the grammar by a factor, polynomial in terms of the number of nonterminals maximally occuring on the right hand side of a production. In this paper, we present an algorithm to generate aλ-free CFG whose total space requirement (or its size) is limited to seven times the initial size. The correctness of our algorithm is established by using a new proof technique based on the structure of the derivation trees and using a counting argument to establish that if a terminal string can be derived in one grammar, it can also be derived in the other.

Keywords and Phrases

Context-free grammar derivation trees equivalent grammar frontier of a derivation tree λ-free CFG 

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References

  1. 1.
    A. V. Aho and J. D. Ullman,The Theory of Parsing, Translation and Compiling, Volume I:Parsing. Prentice Hall, Englewood Cliffs, N.J., 1972.Google Scholar
  2. 2.
    M. Harrison,Introduction to Formal Language Theory. Addison Wesley, Reading, Mass., 1978.Google Scholar
  3. 3.
    H. B. Hunt, D. J. Rosenkrantz and T. G. Szymanski,On the equivalence, containment and covering problems for the regular and context-free languages. Journal of Computer and System Sciences, Vol. 12, 1976, pp. 222–268.Google Scholar

Copyright information

© BIT Foundations 1982

Authors and Affiliations

  • Jainendra Navlakha
    • 1
  1. 1.Department of Mathematical SciencesFlorida International UniversityMiamiUSA

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