We give necessary and sufficient conditions for a language to be the language of finite words that occur infinitely many times in an infinite word.
@article{ITA_2005__39_4_641_0, author = {Thomsen, Klaus}, title = {Languages of finite words occurring infinitely many times in an infinite word}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {39}, year = {2005}, pages = {641-650}, doi = {10.1051/ita:2005033}, mrnumber = {2172143}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2005__39_4_641_0} }
Thomsen, Klaus. Languages of finite words occurring infinitely many times in an infinite word. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) pp. 641-650. doi : 10.1051/ita:2005033. http://gdmltest.u-ga.fr/item/ITA_2005__39_4_641_0/
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