### Abstract

The set of all strings Parikh equivalent to a string in a language L is called the permutation of L. The permutation of a finite n-state DFA (deterministic finite automaton) language over a binary alphabet can be recognized by a DFA with [formula presented] states. We show that if the language consists of equal length binary strings the bound can be improved to f(n)=[formula presented] and for every n congruent to 1 modulo 3 there exists an n-state DFA A recognizing a set of equal length strings such that the minimal DFA for the permutation of L(A) needs f(n) states.

Original language | English |
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Pages (from-to) | 67-78 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 682 |

DOIs | |

Publication status | Published - 2017 Jun 19 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Cho, D. J., Goč, D., Han, Y. S., Ko, S. K., Palioudakis, A., & Salomaa, K. (2017). State complexity of permutation on finite languages over a binary alphabet.

*Theoretical Computer Science*,*682*, 67-78. https://doi.org/10.1016/j.tcs.2017.03.007