Geodesic
Varietés de langages et combinatoire
Séminaire lotharingien de combinatoire, Tome 06 (1982)

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Let A be a finite alphabet. The well-known Kleene's theorem states that a language L of A* is rational iff its syntactic monoid is finite. Schützenberger's theorem states that a language L is star-free iff its syntactic monoid is group-free. It turns out that many subfamilies of the rational languages can be characterized in this way by properties of their syntactic monoids or semigroups. This lecture gives a survey of the various hierarchies of star-free languages, their descriptions in terms of semigroups, and the related decidability results and problems. 

@article{SLC_1982_06_a9,
     author = {Jean-\'Eric Pin},
     title = {Variet\'es de langages et combinatoire},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {06},
     year = {1982},
     url = {http://geodesic.mathdoc.fr/item/SLC_1982_06_a9/}
}
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Jean-Éric Pin. Varietés de langages et combinatoire. Séminaire lotharingien de combinatoire, Tome 06 (1982). http://geodesic.mathdoc.fr/item/SLC_1982_06_a9/