The dot-depth and the polynomial hierarchy correspond on the delta levels

It is well-known that the Sigma_k- and Pi_k-levels of the dot-depth hierarchy and the polynomial hierarchy correspond via leaf languages. In this paper this correspondence will be extended to the Delta_k-levels of these hierarchies: Leaf^P(Delta_k^L) = Delta_k^p

Relating Automata-theoretic Hierarchies to Complexity-theoretic Hierarchies

We show that some natural refinements of the Straubing and Brzozowski hierarchies correspond (via the so called leaf-languages) step by step to similar refinements of the polynomial-time hierarchy. This extends a result of Burtschik and Vollmer on relationship between the Straubing and the polynomial hierarchies. In particular, this applies to the Boolean hierarchy and the plus-hierarchy