### Abstract

We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

Original language | English |
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Title of host publication | Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings |

Pages | 78-89 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2013 Sep 26 |

Event | 15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013 - London, ON, Canada Duration: 2013 Jul 22 → 2013 Jul 25 |

### 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 | 8031 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013 |
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Country | Canada |

City | London, ON |

Period | 13/7/22 → 13/7/25 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings*(pp. 78-89). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8031 LNCS). https://doi.org/10.1007/978-3-642-39310-5_9

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*Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8031 LNCS, pp. 78-89, 15th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2013, London, ON, Canada, 13/7/22. https://doi.org/10.1007/978-3-642-39310-5_9

**State complexity of k-union and k-intersection for prefix-free regular languages.** / Eom, Hae Sung; Han, Yo-Sub; Salomaa, Kai.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - State complexity of k-union and k-intersection for prefix-free regular languages

AU - Eom, Hae Sung

AU - Han, Yo-Sub

AU - Salomaa, Kai

PY - 2013/9/26

Y1 - 2013/9/26

N2 - We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

AB - We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

UR - http://www.scopus.com/inward/record.url?scp=84884475434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884475434&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-39310-5_9

DO - 10.1007/978-3-642-39310-5_9

M3 - Conference contribution

AN - SCOPUS:84884475434

SN - 9783642393099

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 78

EP - 89

BT - Descriptional Complexity of Formal Systems - 15th International Workshop, DCFS 2013, Proceedings

ER -