A Downward Collapse within the Polynomial Hierarchy

Hemaspaandra, Edith; Hemaspaandra, Lane A.; Hempel, Harald

A Downward Collapse within the Polynomial Hierarchy

Authors

Hemaspaandra, Edith

Hemaspaandra, Lane A.

Hempel, Harald

Description

Downward collapse (a.k.a. upward separation) refers to cases where the equality of two larger classes implies the equality of two smaller classes. We provide an unqualified downward collapse result completely within the polynomial hierarchy. In particular, we prove that, for k > 2, if $\psigkone = \psigktwo$ then $\sigmak = \pik = \ph$. We extend this to obtain a more general downward collapse result.
14 pages