  We prove a complexity dichotomy theorem for a class of Holant problems on
3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric
constraint function $f = [x_0, x_1, x_2, x_3]$, we prove that the bipartite
Holant problem $\operatorname{Holant} \left( f \mid \left( =_3 \right) \right)$
is \emph{either} computable in polynomial time \emph{or} $\#$P-hard. The
dichotomy criterion on $f$ is explicit.

Computational Complexity