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

  • Authors:
  • Peter R. J. Asveld

  • Affiliations:
  • Department of Computer Science, Twente University of Technology, AE Enschede, The Netherlands

  • Venue:
  • Theoretical Computer Science - Algebraic methods in language processing
  • Year:
  • 2006

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Abstract

Let Ln be the finite language of all n! strings that are permutations of n different symbols (n ≥ 1). We consider context-free grammars Gn in Chomsky normal form that generate Ln. In particular we study a few families {Gn}n ≥ 1, satisfying L(Gn) = Ln for n ≥ 1, with respect to their descriptional complexity, i.e. we determine the number of nonterminal symbols and the number of production rules of Gn as functions of n.