On the Topological Complexity of Weakly Recognizable Tree Languages

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 < ωω , and pseudoexponentiation with the base ω1 of the Wadge degrees. In consequence, the Wadge hierarchy of weakly recognizable tree languages has the height of at least ε0, that is the least fixed point of the exponentiation with the base ω.

• Type: Conference
• Year: 2007
• Where: FCT
• Authors: Jacques Duparc, Filip Murlak
• Keywords: FCT 2007, Set Theoretic Operations, Tree Languages, Weak Alternating Automata