Abstract:
Derandomization techniques are used to show that at least one of the following holds regarding the size of the counting complexity class SPP. 1. SPP has p-measure 0. 2. PH is contained in SPP. In other words, SPP is small by being a negligible subset of exponential time or large by containing the entire polynomial-time hierarchy. This addresses an open problem about the complexity of the graph isomorphism problem: it is not weakly complete for exponential time unless PH is contained in SPP. It is also shown that the polynomial-time hierarchy is contained in SPP^NP if NP does not have p-measure 0.