The Analytic Polynomial Time Hierarchy

Motivated by results on interactive proof systems we investigate an 9-8-hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the (arithmetic) polynomial-time hierarchy, is called the analytic polynomial-time hierarchy. It is shown that every class of this hierarchy coincides with one of the following classes: pk, pk (k 0), PSPACE, exp k or exp k (k 1). This improves previous results by Orponen [6] and allows interesting comparisons with the above mentioned results on interactive proof systems.