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This paper shows a complete upward collapse in the Polynomial Hierarchy (PH) if for ZPP, two queries to a SAT oracle is equivalent to one query. That is, ZPPSAT = ZPPSAT|| rArr ZPPSAT = PH. These ZPP machines are required to succeed with probability at least 1/2 + 1/p(n) on inputs of length n for some polynomial p(n). This result builds upon recent work by Tripathi who showed a collapse of PH to S2 P. The use of the probability bound of 1/2 + 1/p(n) is justified in part by showing that this bound can be amplified to 1 - 2-nk for ZPPSAT computations. This paper also shows that in the deterministic case, PSAT = PSAT|| rArr PH sube ZPPSAT where the ZPPSAT machine achieves a probability of success of 1/2 - 2-nk.
Date of Conference: 23-26 June 2008