Handbook of theoretical computer science (vol. B)
Theoretical Computer Science
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Regular languages and partial commutations
Information and Computation
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The paper deals with star-free languages in free monoids and trace monoids. We introduce the notion of star-free star, fundamental for this paper, and show that the classes of star-free languages and star-free star languages coincide. Then, using this result, we obtain a general characterization of star-free trace languages, containing a result of Guaiana/Restivo/Salemi (star-free=aperiodic in trace monoids), originally proved in a more involved, combinatorial way.