### Abstract

Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\geq1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\{G_n\}_{n\geq1}$, satisfying $L(G_n)=L_n$ for $n\geq1$, 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 function of $n$.

Original language | Undefined |
---|---|

Pages (from-to) | 118-130 |

Number of pages | 13 |

Journal | Theoretical computer science |

Volume | 354 |

Issue number | 2/1 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

- MSC-68Q45
- MSC-68Q42
- EWI-2711
- METIS-238004
- HMI-SLT: Speech and Language Technology
- IR-55941

## Cite this

Asveld, P. R. J. (2006). Generating all permutations by context-free grammars in Chomsky normal form.

*Theoretical computer science*,*354*(2/1), 118-130. https://doi.org/10.1016/j.tcs.2005.11.010