On the Power of Probabilistic Polynomial Time:PNP[log] ⊆ PP

@inproceedings{Hemachandra1988OnTP,
  title={On the Power of Probabilistic Polynomial Time:PNP[log] ⊆ PP},
  author={L. Hemachandra and Gerd Wechsung},
  year={1988}
}
We show that every set in the 0~ level of the polynomial hierarchy-every set polynomial­ time truth-table reducible to SAT~is accepted by a probabilistic polynomial-time Turing machine: pNP[log] ~ PP. Relatedly, we show that probabilistic polynomial time is closed under polynomial-time parity reductions. 

On the power of parity polynomial time

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  • Computer Science
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The basic techniques for using polynomials in complexity theory are examined, emphasizing intuition at the expense of formality and closure properties, upper bounds, and lower bounds obtained.

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  • Mathematics, Computer Science
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  • 1991
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    J. Comput. Syst. Sci.
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On polynomially many queries to NP or QMA oracles

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PP is as Hard as the Polynomial-Time Hierarchy

It is shown that every set in PH is polynomial-time Turing reducible to a set in PP, and PH is included in BP, which implies a collapse of PH.

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