  We analyze a class of non-simple exclusion processes and the corresponding
growth models by generalizing Gaertners Cole-Hopf transformation. We identify
the main non-linearity and eliminate it by imposing a gradient type condition.
For hopping range at most 3, using the generalized transformation, we prove the
convergence of the exclusion process toward the Kardar-Parisi-Zhang (KPZ)
equation. This is the first universality result concerning interacting particle
systems in the context of KPZ universality class. While this class of exclusion
processes are not explicitly solvable, we obtain the exact one-point limiting
distribution for the step initial condition by using the previous result of
Amir et al. (2011) and our convergence result.
