### Abstract

A string x is an outfix of a string y if there is a string w such that x_1wx_2 = y and x = x_1x_2. A set X of strings is outfix-free if no string in X is an outfix of any other string in X. Based on the properties of outfix strings, we develop a polynomial-time algorithm that determines outfix-freeness of regular languages. Note that outfix-free regular languages are always finite. We consider two cases: 1) a language is given as a finite set of strings and 2) a language is given by a finite-state automaton. Furthermore, we investigate the prime outfix-free decomposition of outfixfree regular languages and design a linear-time algorithm that computes prime outfix-free decomposition for outfix-free regular languages. We also demonstrate the uniqueness of prime outfix-free decomposition.

Original language | English |
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Pages (from-to) | 441-457 |

Number of pages | 17 |

Journal | Fundamenta Informaticae |

Volume | 81 |

Issue number | 4 |

Publication status | Published - 2007 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

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## Cite this

*Fundamenta Informaticae*,

*81*(4), 441-457.