We study the damage spreading in the one-dimensional Ising model by means of the stochastic dynamics resulting from coupling the system and its replica by a family of algorithms that interpolate between the heat bath and the Hinrichsen-Domany algorithms. At high temperatures the dynamics is exactly mapped to the Domany-Kinzel probabilistic cellular automaton. Using a mean-field approximation and Monte Carlo simulations we find the critical line that separates the phase where the damage spreads from the one where it does not.
