Syntactically, this has the same relationship to PostBPPcc as UPPcc does to PPcc; i.e., we only allow private (no public) randomness, and do not charge for α in the cost of a protocol.
Contains PNPcc and hence does not equal PostBPPcc since it has been shown that PNPcc is not contained in PPcc much less in PostBPPcc [BVW07].
Contained in UPPcc.
Not contained in PPcc [BVW07].
Does not contain BPPcc if partial functions are allowed [PPS14].
Contained in UPostBPPcc.