Here, Alice and Bob collectively constitute "Arthur", and the cost of an MAcc communication protocol is defined as the bit length of Merlin's message plus the communication cost of the ensuing randomized protocol between Alice and Bob. (Not charging for the length of Merlin's message would enable every function to be computed with constant cost in this model.)
Does not contain coNPcc (first shown by [Kla03]).
It is open to prove that there exists an explicit two-party function whose MAcc-type communication complexity is ω(n1/2).
The corresponding model consists of randomized protocols such that yes-inputs are accepted with probability at least α and no-inputs are accepted with probability at most α/2 where α is to be thought of as a function of n. The cost of a protocol is defined to be its communication cost plus log(1/α).
Does not contain coNPcc [Raz92] [GW14].
Contains MAcc but does not equal it, since SBPcc is not closed under intersection [GLM+15].
Contained in AMcc and in PostBPPcc.
The complexity measure corresponding to SBPcc is equivalent to the "corruption bound" [GW14].