# An upper bound on the complexity of recognizable tree languages

@article{Finkel2015AnUB, title={An upper bound on the complexity of recognizable tree languages}, author={Olivier Finkel and Dominique Lecomte and Pierre Simonnet}, journal={ArXiv}, year={2015}, volume={abs/1503.02840} }

The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\omega$ into the class ${\bf\Delta}^1\_2$, and the notions of Wadge degree and Veblen function, we argue that this…

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