  A symmetric tensor is completely positive (CP) if it is a sum of tensor
powers of nonnegative vectors. This paper characterizes completely positive
binary tensors. We show that a binary tensor is completely positive if and only
if it satisfies two linear matrix inequalities. This result can be used to
determine whether a binary tensor is completely positive or not. When it is, we
give an algorithm for computing its cp-rank and the decomposition. When the
order is odd, we show that the cp-rank decomposition is unique. When the order
is even, we completely characterize when the cp-rank decomposition is unique.
We also discuss how to compute the nearest cp-approximation when a binary
tensor is not completely positive.
