### 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 |
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Pages (from-to) | 2-12 |

Number of pages | 11 |

Journal | Theoretical Computer Science |

Volume | 610 |

DOIs | |

Publication status | Published - 2016 Jan 11 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*610*, 2-12. https://doi.org/10.1016/j.tcs.2015.04.017