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Outfixfree regular languages and prime outfixfree decomposition
 PROCEEDINGS OF ICTAC’05, LNCS 3722
, 2005
"... 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 outfixfree if no string in X is an outfix of any other string in X. We examine the outfixfree regular languages. Based on the properties of outfix strings, we develop a polyno ..."
Abstract

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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 outfixfree if no string in X is an outfix of any other string in X. We examine the outfixfree regular languages. Based on the properties of outfix strings, we develop a polynomialtime algorithm that determines the outfixfreeness 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 finitestate automaton. Furthermore, we investigate the prime outfixfree decomposition of outfixfree regular languages and design a lineartime prime outfixfree decomposition algorithm for outfixfree regular languages. We demonstrate the uniqueness of prime outfixfree decomposition.