  A collaborative distributed binary decision problem is considered. Two
statisticians are required to declare the correct probability measure of two
jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and
$Y^n=(Y_1,\dots,Y_n)$, out of two possible probability measures on finite
alphabets, namely $P_{XY}$ and $P_{\bar{X}\bar{Y}}$. The marginal samples given
by $X^n$ and $Y^n$ are assumed to be available at different locations. The
statisticians are allowed to exchange limited amount of data over multiple
rounds of interactions, which differs from previous work that deals mainly with
unidirectional communication. A single round of interaction is considered
before the result is generalized to any finite number of communication rounds.
A feasibility result is shown, guaranteeing the feasibility of an error
exponent for general hypotheses, through information-theoretic methods. The
special case of testing against independence is revisited as being an instance
of this result for which also an unfeasibility result is proven. A second
special case is studied where zero-rate communication is imposed (data
exchanges grow sub-exponentially with $n$) for which it is shown that
interaction does not improve asymptotic performance.
