  The critical behavior at the frozen/active transition in the Domany-Kinzel
stochastic cellular automaton (DKCA) is studied {\it via} a surface growth
process in (1+1) dimensions. At criticality, this process presents a kinetic
roughening transition; we measure the critical exponents in simulations. Two
update schemes are considered: in the symmetric scheme, the growth surfaces
belong to the Directed Percolation (DP) universality class, except at one
terminal point. At this point, the phase transition is discontinuous and the
surfaces belong to the Compact Directed Percolation universality class. The
relabeling of space-time points in the nonsymmetric scheme alters the surface
growth dramatically. The critical behavior of rough surfaces at the
nonchaotic/chaotic transition is also studied using the damage spreading
technique; the exponents confirm DP values for the symmetric scheme.
