Abstract
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 DP, the second level of the Boolean Hierarchy (BH). Previous work showed that BH ∶DP⇒ coNP ∶ NP/poly. The stronger assumption that PH ∶ DP 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 ∶ BH2k ⇔ coNP ∶ NP/k
where BH2k denotes the 2k-th level of BH and NP/k denotes the class NP with k-bit advice functions.
Supported in part by the University of Maryland Institute for Advanced Computer Studies.
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Buhrman, H., Chang, R., Fortnow, L. (2003). One Bit of Advice. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_48
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DOI: https://doi.org/10.1007/3-540-36494-3_48
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