## Abstract

The reversal operation is well-studied in the 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 (respectively, prefix-inversion) of a language L consists of all strings ux^{R}v such that uxv∈L (respectively, all strings u^{R}x where ux∈L). We show that the nondeterministic state complexity of prefix-inversion is Θ(n^{2}) and that of inversion is Θ(n^{3}). We show that the deterministic state complexity of prefix-inversion is at most 2^{n⋅logn+n} and has lower bound 2^{Ω(nlogn)}. The same lower bound holds for the state complexity of inversion, but for inversion we do not have a matching upper bound. We also study the state complexity of other variants of the inversion operation.

Original language | English |
---|---|

Pages (from-to) | 2-12 |

Number of pages | 11 |

Journal | Theoretical Computer Science |

Volume | 610 |

DOIs | |

State | Published - 11 Jan 2016 |

## Keywords

- Finite automata
- Inversion operations
- Regular languages
- State complexity