On shuffle ideals
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 359-384.

A shuffle ideal is a language which is a finite union of languages of the form A * a 1 A * A * a k A * 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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     author = {H\'eam, Pierre-Cyrille},
     title = {On shuffle ideals},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {359--384},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {4},
     year = {2002},
     doi = {10.1051/ita:2003002},
     zbl = {1034.68056},
     mrnumber = {1965422},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2003002/}
}
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Héam, Pierre-Cyrille. On shuffle ideals. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 36 (2002) no. 4, pp. 359-384. doi : 10.1051/ita:2003002. http://www.numdam.org/articles/10.1051/ita:2003002/

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