Amplifying ZPP^SAT[1] and the Two Queries Problem
Richard Chang, Suresh Purini · 2008
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[1]= ZPPSAT||[2]rArr ZPPSAT[1]= 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 S2P. 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-nkfor ZPPSAT[1]computations. This paper also shows that in the deterministic case, PSAT[1]= PSAT||[2]rArr PH sube ZPPSAT[1]where the ZPPSAT[1]machine achieves a probability of success of 1/2 - 2-nk.