  We study a one-dimensional, nonequilibrium Potts-like model which has $q$
symmetric absorbing states. For $q=2$, as expected, the model belongs to the
parity conserving universality class. For $q=3$ the critical behaviour depends
on the dynamics of the model. Under a certain dynamics it remains generically
in the active phase, which is also the feature of some other models with three
absorbing states. However, a modified dynamics induces a parity conserving
phase transition. Relations with branching-annihilating random walk models are
discussed in order to explain such a behaviour.

Statistical Mechanics