## Abstract

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 V_{LR} are introduced to reduce the number of occurrences of nonterminals in production rules.

Original language | English |
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Pages (from-to) | 490-492 |

Number of pages | 3 |

Journal | Information Processing Letters |

Volume | 109 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2009 Apr 30 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

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