  We present a probabilistic cellular automaton with two absorbing states,
which can be considered a natural extension of the Domany-Kinzel model. Despite
its simplicity, it shows a very rich phase diagram, with two second-order and
one first-order transition lines that meet at a tricritical point. We study the
phase transitions and the critical behavior of the model using mean field
approximations, direct numerical simulations and field theory. A closed form
for the dynamics of the kinks between the two absorbing phases near the
tricritical point is obtained, providing an exact correspondence between the
presence of conserved quantities and the symmetry of absorbing states. The
second-order critical curves and the kink critical dynamics are found to be in
the directed percolation and parity conservation universality classes,
respectively. The first order phase transition is put in evidence by examining
the hysteresis cycle. We also study the "chaotic" phase, in which two replicas
evolving with the same noise diverge, using mean field and numerical
techniques. Finally, we show how the shape of the potential of the
field-theoretic formulation of the problem can be obtained by direct numerical
simulations.
