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The results in this paper show that coNP is contained in NP with 1 bit of advice (denoted NP=1) if and only if the Polynomial Hierarchy (PH) collapses to D , the second level of the Boolean Hierarchy (BH). Previous work showed that BH D =) coNP NP=poly. The stronger assumption that PH D in the new result allows the length of the advice function to be reduced to a single bit and also makes the converse true. The one-bit case can be generalized to any constant k: PH BH 2 k ...


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