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


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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Copyright information

© BIT Foundations 1982

Authors and Affiliations

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

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