  We consider the ultra-discrete Burgers equation. All variables of the
equation are discrete. We classify the equation into five regions in the
parameter space. We discuss behavior of solutions. Using this equation we
construct the deterministic surface growth models respectively. Furthermore we
introduce noise into the ultra-discrete Burgers equation. We present the
automata models of the KPZ equation. One model corresponds to the discrete
version of the ASEP and the other to the Kim-Kosterlitz model.
