Class Description

P^NP[k]: P With k NP Queries(for constant k)

Equals P with 2^k-1 parallel queries to NP (i.e. queries that do not depend on the outcomes of previous queries) ([BH91] and [Hem89] independently).

If P^NP[1] = P^NP[2], then P^NP[1] = P^NP[log] and indeed PH collapses to Δ₃P (attributed in [Har87b] to J. Kadin).

Linked From

P^NP[log]: P With Log NP Queries

Also known as Θ₂^P.

The class of decision problems solvable by a P machine, that can make O(log n) queries to an NP oracle (where n is the length of the input).

Equals P^||NP, the class of decision problems solvable by a P machine that can make polynomially many nonadaptive queries to an NP oracle (i.e. queries that do not depend on the outcomes of previous queries) ([BH91] and [Hem89] independently).

P^NP[log] is contained in PP [BHW89].

Determining the winner in an election system proposed in 1876 by Charles Dodgson (a.k.a. Lewis Carroll) has been shown to be complete for P^NP[log] [HHR97].

Contains P^NP[k] for all constants k.

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