Two Remarks on the Power of Counting
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...
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| Published: |
2023
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| Online Access: | https://hdl.handle.net/1721.1/149038 |
| Summary: | 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. |
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