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Star-free Star and Trace Languages

100%

Ochmański E. , Stawikowska K.

Fundamenta Informaticae

2006

tom Vol. 72, nr 1-3

323-331

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.

On the Shuffle of Star-Free Languages

70%

Castiglione G. , Restivo A.

Fundamenta Informaticae

2012

tom Vol. 116, nr 1-4

35-44

Motivated by the general problem to characterize families of languages closed under shuffle, we investigate some conditions under which the shuffle of two star-free languages is starfree. Some of the special cases here approached give rise to new problems in combinatorics on words.