## Outfix-free regular languages and prime outfix-free decomposition (2005)

Venue: | PROCEEDINGS OF ICTAC’05, LNCS 3722 |

Citations: | 5 - 4 self |

### BibTeX

@INPROCEEDINGS{Han05outfix-freeregular,

author = {Yo-sub Han and Derick Wood},

title = { Outfix-free regular languages and prime outfix-free decomposition},

booktitle = {PROCEEDINGS OF ICTAC’05, LNCS 3722},

year = {2005},

pages = {96--109},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

A string x is an outfix of a string y if there is a string w such that x1wx2 = y, wherex = x1x2 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.

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Citation Context ...o examine outfix-free regular languages and the prime outfix-free decomposition problem. Note that Ito and his co-researchers [12] showed that an outfix-free regular language is finite and Han et al. =-=[7]-=- demonstrated that the family of outfix-free regular languages is a proper subset of the family of simple-regular languages. On the other hand, there was no known efficient algorithm to determine whet... |

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Citation Context ...phy, information transmission and so on [14]. They are categorized with respect to different conditions (for example, prefix-free, suffixfree, infix-free or outfix-free) according to the applications =-=[11,12,13,15]-=-. Since a code is a set of strings, it is a language. The conditions that classify code types define proper subfamilies of given language families. For regular languages, for example, prefix-freeness ... |

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Citation Context ...fix-free if, for all distinct strings x, y, z ∈ Σ ∗ , xz ∈ L and xyz ∈ L imply y = λ. – hyper if L is infix-free and outfix-free. For further details and definitions, refer to Ito et al. [12] or Shyr =-=[18]-=-. We say that a regular expression E is outfix-free if L(E) is outfix-free. The language defined by such an outfix-free regular expression is called an outfixfree regular language. In a similar way, w... |