### Abstract

A string x is an outfix of a string y if there is a string w such that x _{1}wx _{2} = y, where x = x _{1}x _{2} and a set X of strings is outfix-free if no string in X is an outfix of any other string in X. We examine the outfix-free regular languages. Based on the properties of outfix strings, we develop a polynomial-time algorithm that determines the outfix-freeness of regular languages. We consider two cases: A language is given as a set of strings and a language is given by an acyclic deterministic finite-state automaton. Furthermore, we investigate the prime outfix-free decomposition of outfix-free regular languages and design a linear-time prime outfix-free decomposition algorithm for outfix-free regular languages. We demonstrate the uniqueness of prime outfix-free decomposition.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 96-109 |

Number of pages | 14 |

DOIs | |

Publication status | Published - 2005 |

Event | 2nd International Colloquium on Theoretical Aspects of Computing - ICTAC 2005 - Hanoi, Viet Nam Duration: 2005 Oct 17 → 2005 Oct 21 |

### 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 | 3722 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Colloquium on Theoretical Aspects of Computing - ICTAC 2005 |
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Country | Viet Nam |

City | Hanoi |

Period | 05/10/17 → 05/10/21 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 96-109). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3722 LNCS). https://doi.org/10.1007/11560647_6