Outfix-Free Regular Languages and Prime Outfix-Free Decomposition
نویسندگان
چکیده
A string x is an outfix of a string y if there is a string w such that x1wx2 = y and x = x1x2. 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.
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