An elementary proof of a generalization of double Greibach normal form

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3 Citations (Scopus)


Greibach normal form (GNF) introduced by Greibach, which facilitates proving several properties of context-free languages, is studied. Double Greibach normal form is a variant of GNF, where the right-hand side of each production begins and ends with a terminal symbol. Engelfriet has given an elementary proof of double GNF, while Rosenkrantz's and Hotz's proofs involve higher algebraic techniques. One can easily convert any CFG G = (V , T , P, S) in double GNF into an equivalent CFG in (m,n)-GNF for any nonnegative integers m and n such that at least one of them is not zero, by letting the new grammar consist of the rules such that α is derived from A by at most m steps of left-most derivation and at most n steps of right-most derivation. New nonterminals representing sequences of nonterminals from VLR are introduced to reduce the number of occurrences of nonterminals in production rules.

Original languageEnglish
Pages (from-to)490-492
Number of pages3
JournalInformation Processing Letters
Issue number10
Publication statusPublished - 2009 Apr 30
Externally publishedYes


  • Context-free grammars
  • Formal languages
  • Greibach normal form

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


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