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 H.-J. Burtschik and H. Vollmer on relationship between the Straubingand the polynomial hierarchies. In particular, this applies to the boolean hierarchy and the plus-hierarchy.

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