Generating all permutations by context-free grammars in Greibach normal form

Abstract

We consider context-free grammars G n in Greibach normal form and, particularly, in Greibach m -form ( m = 1 , 2 ) which generates the finite language L n of all n ! strings that are permutations of n different symbols ( n ≥ 1 ). These grammars are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols and the number of production rules of G n as functions of n . As in the case of Chomsky normal form, these descriptional complexity measures grow faster than any polynomial function.