### Abstract

It appears that the state complexity of each combined operation has its own special features. Thus, it is important and practical to obtain good estimates for some commonly used general cases. In this paper, we consider the state complexity of combined Boolean operations and give an exact bound for all of them in the case when the alphabet is not fixed. Moreover, we show that for any fixed alphabet, this bound can be reached in infinitely many cases. We also consider the state complexity of multiple catenations. The state complexities are obtained in the cases of the catenations of three and four languages. An estimate for the catenation of an arbitrary number of languages is given, which is very close to the state complexities in the three and four languages cases.

Original language | English |
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Title of host publication | Descriptional Complexity of Formal Systems - 10th International Workshop, DCFS 2008 |

Publisher | University of Prince Edward Island |

Pages | 168-181 |

Number of pages | 14 |

ISBN (Print) | 9780919013568 |

Publication status | Published - Jan 1 2008 |

Event | 10th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2008 - Charlottetown, PE, Canada Duration: Jul 16 2008 → Jul 18 2008 |

### Publication series

Name | Descriptional Complexity of Formal Systems - 10th International Workshop, DCFS 2008 |
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### Other

Other | 10th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2008 |
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Country | Canada |

City | Charlottetown, PE |

Period | 7/16/08 → 7/18/08 |

### Keywords

- Boolean operations
- Cate- nation
- Combined operations
- Estimation
- Multiple operations
- State complexity

### ASJC Scopus subject areas

- Software

### Cite this

*Descriptional Complexity of Formal Systems - 10th International Workshop, DCFS 2008*(pp. 168-181). (Descriptional Complexity of Formal Systems - 10th International Workshop, DCFS 2008). University of Prince Edward Island.