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

  • Authors:
  • Peter R. J. Asveld

  • Affiliations:
  • Department of Computer Science, Twente University of Technology, P.O. Box 217, 7500 AE Enschede, The Netherlands

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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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.