可识别树语言复杂度的一个上界
An Upper Bound on the Complexity of Recognizable Tree Languages
摘要：
第三作者在他1992年的博士论文[Sim92]中注意到，无限树的每一个正则树语言都属于某个自然数$n\geq 1$的类$\Game (D\_n({\bfΣ}^0\_2))$，其中$\Game$是游戏量词。我们首先对这个结果作了详细的说明。其次，通过将Cantor空间$2^ω$的非自对偶Borel子集的Wadge层次嵌入到类${\bfΔ}^1\_2$中，并引入Wadge度和Veblen函数的概念，证明了正则树语言的拓扑复杂度的上界比通常的${\bfΔ}^1\_2$好得多.
英文摘要：
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bfΣ}^0\_2))$ 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 $2^ω$ into the class ${\bfΔ}^1\_2$, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ${\bfΔ}^1\_2$.
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