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

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2 Author(s)
Chang, R. ; Dept. of Comput. Sci. & Electr. Eng., Univ. of Maryland Baltimore County, Baltimore, MD ; Purini, S.

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 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[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.

Published in:

Computational Complexity, 2008. CCC '08. 23rd Annual IEEE Conference on

Date of Conference:

23-26 June 2008