## Abstract

The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2^{n} (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings ux^{R} v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n ^{3}). We establish that the deterministic state complexity of the inversion is 2^{Ω(n·logn)}, which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.

Original language | English |
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Title of host publication | Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Proceedings |

Publisher | Springer Verlag |

Pages | 102-113 |

Number of pages | 12 |

ISBN (Print) | 9783319097039 |

DOIs | |

Publication status | Published - 2014 |

Event | 16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014 - Turku, Finland Duration: 2014 Aug 5 → 2014 Aug 8 |

### 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 | 8614 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2014 |
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Country/Territory | Finland |

City | Turku |

Period | 14/8/5 → 14/8/8 |

### Bibliographical note

Funding Information:Cho, Han and Ko were 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 Yonsei University Future-leading Research Initiative of 2014. Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224 .

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)