The Analytic Polynomial-Time Hierarchy

ABSTRACT Motivated by results on interactive proof systems we investigate an ∃-∀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: ∑, Π (k⩾0), PSPACE, ∑ or Π (k⩾1). This improves previous results by Orponen [6] and allows interesting comparisons with the above mentioned results on inter-active proof systems.