Theoretical Computer Science pp 269-275 | Cite as

# Two remarks on the power of counting

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## Abstract

The relationship between the polynomial hierarchy and Valiant's class #P is at present unknown. We show that some low portions of the polynomial hierarchy, namely deterministic polynomial algorithms using an NP oracle at most a logarithmic number of times, can be simulated by one #P computation. We also show that the class of problems solvable by polynomial-time nondeterministic Turing machines which accept whenever there is an odd number of accepting computations is idempotent, that is, closed under usage of oracles from the same class.

## Keywords

Counting problems oracle computation polynomial hierarchy parity problems machine simulation## Preview

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## References

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1982