The Analytic Polynomial-Time Hierarchy

Mathematical Logic Quarterly 44 (4):529-544 (1998)

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 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: ∑math image, Πmath image , PSPACE, ∑math image or Πmath image . This improves previous results by Orponen [6] and allows interesting comparisons with the above mentioned results on inter-active proof systems
Keywords Oracles  Complexity theory  Polynomial‐time hierarchies  Quantifiers  Set operators
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DOI 10.1002/malq.19980440412
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