### 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

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

}

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

**State complexity of permutation on finite languages over a binary alphabet.** / Cho, Da Jung; Goč, Daniel; Han, Yo-Sub; Ko, Sang Ki; Palioudakis, Alexandros; Salomaa, Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - State complexity of permutation on finite languages over a binary alphabet

AU - Cho, Da Jung

AU - Goč, Daniel

AU - Han, Yo-Sub

AU - Ko, Sang Ki

AU - Palioudakis, Alexandros

AU - Salomaa, Kai

PY - 2017/6/19

Y1 - 2017/6/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85017111531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017111531&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2017.03.007

DO - 10.1016/j.tcs.2017.03.007

M3 - Article

VL - 682

SP - 67

EP - 78

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -