This class is parameterized by a constant ε>0. The corresponding model consists of randomized protocols such that yes-inputs are accepted with probability in [(1-ε)α,α] and no-inputs are accepted with probability in [0,α] 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 admit efficient amplification with respect to the ε parameter [GLM+15].
The complexity measure associated with WAPPcc is equivalent to the "(one-sided) smooth rectangle bound" and also to the approximate nonnegative rank of the communication matrix [KMSY14].
Syntactically, this has the same relationship to WAPPcc 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. However, it has been shown that UWAPPcc protocols can be efficiently simulated by WAPPcc protocols with a slightly larger ε parameter [GLM+15].