Abstract
Buhrman and Torenvliet created an oracle relative to which P NP=NEXP and thus P NP=P NEXP. Their proof uses a delicate finite injury argument that leads to a nonrecursive oracle. We simplify their proof removing the injury to create a recursive oracle making P NP=NEXP. In addition, in our construction we can make P=UP=NP∩coNP. This leads to the curious situation where LOW(NP)=P but LOW(P NP)=NEXP, and the complete ≤ p m -degree for P NP collapses to a p-isomorphism type.
Partially Supported by NSF Grant CCR-9209833.
Partially Supported by NSF Grant CCR-9253582.
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Fenner, S.A., Fortnow, L.J. (1995). Beyond PNP=NEXP. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_110
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DOI: https://doi.org/10.1007/3-540-59042-0_110
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