Abstract
We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals < ω ω, and pseudo-exponentiation with the base ω 1 of the Wadge degrees. In consequence, the Wadge hierarchy of weakly recognizable tree languages has the height of at least ε 0, that is the least fixed point of the exponentiation with the base ω.
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Duparc, J., Murlak, F. (2007). On the Topological Complexity of Weakly Recognizable Tree Languages. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_23
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DOI: https://doi.org/10.1007/978-3-540-74240-1_23
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