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Cited article:

Going Higher in First-Order Quantifier Alternation Hierarchies on Words

Thomas Place and Marc Zeitoun
Journal of the ACM 66 (2) 1 (2019)
https://doi.org/10.1145/3303991

A SURVEY ON SMALL FRAGMENTS OF FIRST-ORDER LOGIC OVER FINITE WORDS

VOLKER DIEKERT, PAUL GASTIN and MANFRED KUFLEITNER
International Journal of Foundations of Computer Science 19 (03) 513 (2008)
https://doi.org/10.1142/S0129054108005802