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- W2000805093 abstract "The counting class C=P, which captures the notion of “exact counting”, while extremely powerful under various nondeterministic reductions, is quite weak under polynomial-time deterministic reductions. We discuss the analogies between NP and co-C=P, which allow us to derive many interesting results for such deterministic reductions to co-C=P. We exploit these results to obtain some interesting oracle separations. Most importantly, we show that there exists an oracleA such that $$ oplus P^A nsubseteq P^{C_ = P^A } $$ and $$BPP^A nsubseteq P^{C_ = P^A } $$ Therefore, techniques that would prove that C=P and PP are polynomial-time Turing equivalent, or that C=P is polynomial-time Turing hard for the polynomial-time hierarchy, would not relativize." @default.
- W2000805093 created "2016-06-24" @default.
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- W2000805093 date "1993-06-01" @default.
- W2000805093 modified "2023-09-24" @default.
- W2000805093 title "On the power of deterministic reductions to C=P" @default.
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- W2000805093 doi "https://doi.org/10.1007/bf01202284" @default.
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