On Shuffle Ideals

A shuffle ideal is a language which is a finite union of languages of the form A* a 1 A*...A* a k where A is a finite alphabet and the a i 's are letters. We show how to represent shuffle ideals by special automata and how to compute these representations. We also give a temporal logic characterization of shuffle ideals and we study its expressive power over infinite words. We characterize the complexity of deciding whether a language is a shuffle ideal and we give a new quadratic algorithm for this problem. Finally we also present a characterization by subwords of the minimal automaton of a shuffle ideal and study the complexity of basic operations on shuffle ideals.

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