A Reducibility for the Dot-Depth Hierarchy


Victor L. Selivanov
A.P. Ershov Institute of Informatics Systems
Siberian Division of the Russian Academy of Sciences
vseliv@ngs.ru

and

Klaus W. Wagner
Institut für Informatik
Julius-Maximilians-Universität Würzburg
wagner@informatik.uni-wuerzburg.de


Abstract:
Hierarchies considered  in computability theory and in complexity theory are related to some reducibilities in the sense that levels of the hierarchies are downward closed and have complete sets. In this paper we propose a reducibility having similar relationship to the Brzozowski's dot-depth hierarchy and some its refinements. We prove some basic facts on the corresponding degree structure and discuss relationships of the reducibility to complexity theory (via the leaf-language approach).