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1989
Springer

On the Structure of Bounded Queries to Arbitrary NP Sets

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On the Structure of Bounded Queries to Arbitrary NP Sets
Kadin [6] showed that if the Polynomial Hierarchy (PH) has infinitely many levels, then for all k, PSAT[k] ⊂ PSAT[k+1]. This paper extends Kadin’s technique and shows that a proper query hierarchy is not an exclusive property of NP complete sets. In fact, for any A ∈ NP − low3, if PH has infinitely many levels, then PA[k] ⊂ PA[k+1]. Moreover, for the case of parallel queries, PA [k+1] is not even contained in PSAT [k]. These same techniques can be used to explore some other questions about query hierarchies. For example, if there exists any A such that PA[2] = PSAT[1], then PH collapses to ∆P 3 . Key words. Polynomial-time Hierarchy, Boolean Hierarchy, bounded queries, sparse sets, nonuniform computation. AMS(MOS) subject classifications. 68Q15, 03D15, 03D20
Richard Chang
Added 10 Aug 2010
Updated 10 Aug 2010
Type Conference
Year 1989
Where COCO
Authors Richard Chang
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