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

@inproceedings{Beigel1989OnTP,
  title={On the Power of Probabilistic Polynomial Time: PNP[log] subseteq PP},
  author={Richard Beigel and Lane A. Hemaspaandra and Gerd Wechsung},
  booktitle={Structure in Complexity Theory Conference},
  year={1989}
}
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. 

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