We study the Domany-Kinzel model, which is a class of discrete time
Markov processes with two parameters (p_1,p_2) \in [0,1]^2 and whose
states are subsets of Z, the set of integers. When p_1=Ώΐ
and p_2=(2ΐ-ΐ^2) with (Ώ,ΐ) \in [0,1]^2, the process can be
identified with the mixed site-bond oriented percolation model
on a square lattice with the probabilities of open site Ώand of
open bond ΐ. For the attractive case, 0<=p_1<=p_2<=1, the compete
convergence theorem is easily obtained. On the other hand,
the case (p_1,p_2)=(1,0) realizes the rule 90 cellular automaton
of Wolframe in which, starting form the Bernoulli measure with density \theta,
the distribution converges weakly only if \theta \in {0,1/2,1}.
Using our new construction of processes based on signed measures,
we prove limit theorems which are also valid for non-attractive case
with (p_1,p_2) = (1,0). In particular, when p_2 \in [0,1] and p_1 is close to 1,
the complete convergence theorem is obtained as a corollary of the limit theorems.
