### 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 |
---|---|

Pages (from-to) | 441-457 |

Number of pages | 17 |

Journal | Fundamenta Informaticae |

Volume | 81 |

Issue number | 4 |

Publication status | Published - 2007 Dec 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Fundamenta Informaticae*,

*81*(4), 441-457.

}

*Fundamenta Informaticae*, vol. 81, no. 4, pp. 441-457.

**Outfix-free regular languages and prime outfix-free decomposition.** / Han, Yo-Sub; Wood, Derick.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Outfix-free regular languages and prime outfix-free decomposition

AU - Han, Yo-Sub

AU - Wood, Derick

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38049119795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38049119795&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:38049119795

VL - 81

SP - 441

EP - 457

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 4

ER -