Comparative complexity of grammar forms

Abstract

The definition of “grammar form” introduced in [CG] makes it possible to state and prove results about various types of grammars in a uniform way. Among questions naturally formalizable in this framework are many about the complexity or efficiency of grammars of different kinds. Grammar forms provide a reasonable way of considering the totality of other forms we might use, and so answering the question with both upper and lower bound results. The general question considered in this paper is the following: which grammar forms are more efficient than other grammar forms for the expression of classes of languages, and how much gain in efficiency is possible? Our results deal solely with context-free grammars, and use both derivation complexity and size of grammars as complexity measures.