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

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.