## Abstract

We investigate the state complexity of the permutation operation over finite binary languages. We first give an upper bound of the state complexity of the permutation operation for a restricted case of these languages. We later present a general upper bound of the state complexity of permutation over finite binary languages, which is asymptotically the same as the previous case. Moreover, we show that there is a family of languages that the minimal DFA recognizing each of these languages needs at least as many states as the given upper bound for the restricted case. Furthermore, we investigate the state complexity of permutation by focusing on the structure of the minimal DFA.

Original language | English |
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Title of host publication | Descriptional Complexity of Formal Systems - 17th International Workshop, DCFS 2015, Proceedings |

Editors | Alexander Okhotin, Jeffrey Shallit |

Publisher | Springer Verlag |

Pages | 220-230 |

Number of pages | 11 |

ISBN (Print) | 9783319192246 |

DOIs | |

Publication status | Published - 2015 |

Event | 17th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2015 - Waterloo, Canada Duration: 2015 Jun 25 → 2015 Jun 27 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9118 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2015 |
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Country/Territory | Canada |

City | Waterloo |

Period | 15/6/25 → 15/6/27 |

### Bibliographical note

Funding Information:This research was supported by the Basic Science Research Program through NRF funded by MEST (2012R1A1A2044562), the International Cooperation Program managed by NRF of Korea (2014K2A1A2048512) and the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.

Publisher Copyright:

© Springer International Publishing Switzerland 2015.

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)