no. 1
Characterizing the polynomial hierarchy by alternating auxiliary pushdown automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 23 (1989) no. 1, pp. 87-99. 
@article{ITA_1989__23_1_87_0,
     author = {Jenner, Birgit and Kirsig, Bernd},
     title = {Characterizing the polynomial hierarchy by alternating auxiliary pushdown automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {87--99},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {1},
     year = {1989},
     mrnumber = {990069},
     zbl = {0665.68038},
     language = {en},
     url = {http://archive.numdam.org/item/ITA_1989__23_1_87_0/}
}
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Jenner, Birgit; Kirsig, Bernd. Characterizing the polynomial hierarchy by alternating auxiliary pushdown automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 23 (1989) no. 1, pp. 87-99. http://archive.numdam.org/item/ITA_1989__23_1_87_0/

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