Outfix-Free Regular Languages and Prime Outfix-Free Decomposition

Authors:
Yo-Sub Han;Derick Wood
Affiliations:
Intelligence and Interaction Research Center, Korea Institute of Science and Technology, P.O. BOX 131, Cheongryang, Seoul, Korea. E-mail: emmous@kist.re.kr;Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR. E-mail: dwood@cs.ust.hk
Venue:
Fundamenta Informaticae
Year:
2007

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Abstract

A string x is an outfix of a string y if there is a string wsuch that x_1wx_2 = y and x = x_1x_2. A set X of strings isoutfix-free if no string in X is an outfix of any other string inX. Based on the properties of outfix strings, we develop apolynomial-time algorithm that determines outfix-freeness ofregular languages. Note that outfix-free regular languages arealways finite. We consider two cases: 1) a language is given as afinite set of strings and 2) a language is given by a finite-stateautomaton. Furthermore, we investigate the prime outfix-freedecomposition of outfixfree regular languages and design alinear-time algorithm that computes prime outfix-free decompositionfor outfix-free regular languages. We also demonstrate theuniqueness of prime outfix-free decomposition.