Amplifying ZPP^SAT[1] and the Two Queries Problem

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] = 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 [16] who showed a collapse of PH to SP 2. 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[1] computations. This paper also shows that in the deterministic case, PSAT[1] = PSAT [2] = PH ZPPSAT[1] where the ZPPSAT[1] machine achieves a probability of success of 1/2 -2-nk .

• Type: Conference
• Year: 2008
• Where: COCO
• Authors: Richard Chang, Suresh Purini
• Keywords: Algorithms, COCO 2008, Complete Upward Collapse, Polynomial Hierarchy, SAT Oracle