# 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.

## 21 Citations

### On the power of parity polynomial time

- Computer ScienceMathematical systems theory
- 2005

It is proved that the complexity class ⊕P, parity polynomial time [PZ], contains the class of languages accepted byNP machines with few accepting paths, and that theclass of nondeterministic path-restricted languages is closed under bounded truth-table reductions.

### Restricted Relativizations of Probablistic Polynomial Time

- Computer Science, MathematicsTheor. Comput. Sci.
- 1992

### The polynomial method in circuit complexity

- Computer Science[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference
- 1993

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.

### Exponential-Time and Subexponential-Time Sets

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1993

### Counting classes are at least as hard as the polynomial-time hierarchy

- Mathematics, Computer Science[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference
- 1991

It is shown that many natural counting classes are at least as computationally hard as PH in the following sense: for each K of the counting classes, every set in K(PH) is polynomial-time randomized many-one reducible to a set inK with two-sided exponentially small error probability.

### Polynomial Time 1-Turing Reductions from #PH to #P

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1992

### Perceptrons, PP, and the polynomial hierarchy

- Computer Science[1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference
- 1992

AbstractWe construct a predicate that is computable by a perceptron with linear size, order 1, and exponential weights, but which cannot be computed by any perceptron having subexponential…

### On polynomially many queries to NP or QMA oracles

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2021

This work shows that for any veriﬁcation class C, any P C machine with a query graph of “separator number” s can be simulated using deterministic time exp, and shows how to combine Gottlob’s “admissible-weighting function’ framework with the “ﬂag-qubit” framework for embedding P C computations directly into APX-SIM instances in a black-box fashion.

### PP is as Hard as the Polynomial-Time Hierarchy

- Computer ScienceSIAM J. Comput.
- 1991

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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