Polynomial hierarchy

Known as: Polynomial time hierarchy, Polynomial-time hierarchy 
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes… (More)
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AC0Analytical hierarchyArthur–Merlin protocolBelief revision
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Highly Cited
2011
Highly Cited
2011
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
  • M ICHAEL J. B REMNER, R ICHARD J OZSA
  • 2011
We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that… (More)
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Highly Cited
2009
Highly Cited
2009
On problems without polynomial kernels
Kernelization is a strong and widely-applied technique in parameterized complexity. In a nutshell, a kernelization algorithm, or… (More)
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Highly Cited
2009
Highly Cited
2009
BQP and the polynomial hierarchy
The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence… (More)
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Highly Cited
1992
Highly Cited
1992
Counting Classes are at Least as Hard as the Polynomial-Time Hierarchy
In this paper, it is shown that many natural counting classes, such as PP, C=P, and MODkP, arc at least as computationally hard… (More)
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Highly Cited
1991
Highly Cited
1991
PP is as Hard as the Polynomial-Time Hierarchy
In this paper, two interesting complexity classes, PP and P, are compared with PH, the polynomial-time hierarchy. It is shown… (More)
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Highly Cited
1988
Highly Cited
1988
The Polynomial Time Hierarchy Collapses if the Boolean Hierarchy Collapses
It is shown that if the Boolean hierarchy (BH) collapses, then there exists a sparse set S such that co-NP C_ NPs, and therefore… (More)
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Review
1986
Review
1986
The Polynomial Hierarchy and Intuitionistic Bounded Arithmetic
Intuitionistic theories IS: of Bounded Arithmetic a re introduced and i t is shown tha t the definable functions of IS: a re… (More)
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Highly Cited
1985
Highly Cited
1985
Separating the polynomial-time hierarchy by oracles
We present exponential lower bounds on the size of depth-k Boolean circuits for computing certain functions. These results imply… (More)
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Highly Cited
1983
Highly Cited
1983
BPP and the Polynomial Hierarchy
We start with some definitions about probabilistic Turing machines (for a detailed exposition of this subject the reader is… (More)
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Highly Cited
1981
Highly Cited
1981
Parity, circuits, and the polynomial-time hierarchy
A function f is realizable in bounded depth and g(n) size .if there is a sequence of circuits 0 1 , C2 ,.·•• mane np of !\,V, and… (More)
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