We define simple-regular expressions and languages. Simple-regular languages pro- vide a necessary condition for a language to be outfix-free. We design algorithms that compute simple-regular languages from finite-state automata. Furthermore, we inves- tigate the complexity blowup from a given finite-state automaton to its simple-regular language automaton and show that there is an exponential blowup. In addition, we present a finite-state automata construction for simple-regular expressions based on state expansion.
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[Show abstract][Hide abstract]ABSTRACT: A string x is an outfix of a string y if there is a string w such that x
2=y, where x = x
2 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.