The one-dimensional Domany-Kinzel cellular automaton is investigated by two numerical approaches: (i) the spontaneous-search method, which is a method appropriated for a search of criticality; (ii) short-time dynamics. Both critical frontiers of the system are investigated, namely, the one separating the frozen and active phases, as well as the critical line determined by damage spreading between two cellular automata, that splits the active phase into the nonchaotic and chaotic phases. The efficiency of the spontaneous-search method is established herein through a precise estimate of both critical frontiers, and in addition to that, it is shown that this method may also be used in the determination of the critical exponent ν ⊥ . Using the critical frontiers obtained, other exponents are estimated through short-time dynamics. It is verified that the critical exponents of both critical frontiers fall in the universality class of directed percolation. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200805.70.Ln Nonequilibrium and irreversible thermodynamics, 64.60.Ht Dynamic critical phenomena, 64.60.-i General studies of phase transitions,
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