Conference Paper

Simple-Regular Expressions and Languages.

Conference: 7th International Workshop on Descriptional Complexity of Formal Systems - DCFS 2005, Como, Italy, June 30 - July 2, 2005. Proceedings
Source: DBLP


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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    ABSTRACT: As tringx is an outfix of a string y if there is a string w such that x1wx2 = y ,w herex = 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 decom- position 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.
    Theoretical Aspects of Computing - ICTAC 2005, Second International Colloquium, Hanoi, Vietnam, October 17-21, 2005, Proceedings; 01/2005

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