2 research outputs found
Transfinite Extension of the Mu-Calculus
In [1] Bradfield found a link between finite differences formed by Sigma(2)(0) sets and the mu-arithmetic introduced by Lubarski [7]. We extend this approach into the transfinite: in allowing countable disjunctions we show that this kind of extended mu-calculus matches neatly to the transfinite difference hierarchy of E-2(0) sets. The difference hierarchy is intimately related to parity games. When passing to infinitely many priorities, it might not longer be true that there is a positional winning strategy. However, if such games are derived from the difference hierarchy, this property still holds true
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where 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
into the class , 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