We introduce two kinds of discrete-time non-equilibrium lattice models (stochastic cellular automata), which we call the creation process eta(t) and the branching process <(eta)over bar>(t). In special cases the former process can be identified with the site or bond directed percolation models. When the system is defined on a d-dimensional finite lattice with size L, these processes are determined by 2(Ld) x 2(Ld) transition matrices, M(L) and M(L), respectively. It is proved that subject to certain relations between the parameters of these models, M(L) and the transpose of M(L) are conjugate and thus the characteristic polynomials become equal to each other, det(M(L) - lambda E) = det(M(L) - lambda E), for arbitrary L greater than or equal to n, where E is the identity matrix. Since dynamical critical exponents as well as critical values will be determined by the asymptotic behaviour in the limit L --> infinity of the large eigenvalues of the transition matrix, our result implies that, if continuous phase transitions and critical phenomena are observed, these two processes belong to the same universality class. In proving the equality, we use the relation which is called the coalescing duality in probability theory.