A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2]

@inproceedings{Duparc2015ATA,
  title={A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2]},
  author={Jacques Duparc and Kevin Fournier},
  booktitle={DCFS},
  year={2015}
}
We provide a hierarchy of tree languages recognised by nondeterministic parity tree automata with priorities in \(\{0,1,2\}\), whose length exceeds the first fixed point of the \(\varepsilon \) operation (that itself enumerates the fixed points of \(x\mapsto \omega ^x\)). We conjecture that, up to Wadge equivalence, it exhibits all regular tree languages of index \([0,2]\). 
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