Parallel Time and Quantifier Prefixes

We characterize the amount of alternation between blocks of Boolean quantifiers (having both existential and universal), blocks of real existential quantifiers, and blocks of real universal quantifiers that can be decided in parallel polynomial time over the reals. We do so under the assumption that blocks have a uniform bound on their size, both for the case of this bound to be polynomial and constant. On the way towards this characterization we prove a real version of Savitch’s Theorem.