The μ-calculus alternation-depth hierarchy is strict on binary trees
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 4-5, pp. 329-339. 
@article{ITA_1999__33_4-5_329_0,
     author = {Arnold, Andr\'e},
     title = {The $\mu $-calculus alternation-depth hierarchy is strict on binary trees},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {329--339},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {4-5},
     year = {1999},
     mrnumber = {1748659},
     zbl = {0945.68118},
     language = {en},
     url = {http://www.numdam.org/item/ITA_1999__33_4-5_329_0/}
}
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Arnold, André. The $\mu $-calculus alternation-depth hierarchy is strict on binary trees. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 4-5, pp. 329-339. http://www.numdam.org/item/ITA_1999__33_4-5_329_0/

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