Error-bounded probabilistic computations between MA and AM

We introduce the probabilistic class SBP which is defined in a BPP-like manner. This class emerges from BPP by keeping the promise of a probability gap but decreasing the probability limit from 1/2 to exponentially small values. We show that SBP is in the polynomial-timehierarchy, exactly between the Arthur-Merlin classes MA and AM on one the hand and between BPP and the threshold class BPPpath on the other hand. We provide evidence that SBP does not coincide with these and other known complexity classes. In particular, in a suitable relativized world, SBP is not contained in P 2 . As a consequence we get the same for BPPpath. This solves an open question raised by Han et al. [HHT97].

• Type: Journal
• Year: 2006
• Where: JCSS
• Authors: Elmar Böhler, Christian Glaßer, Daniel Meister
• Keywords: Arthur-merlin Classes Ma, JCSS 2006, Probabilistic Class Sbp, Probability Gap