  We analyze a two-offspring Branching Annihilating Random Walk ($n=2$ BAW)
model, with finite annihilation rate. The finite annihilation rate allows for a
dynamical phase transition between a vacuum, absorbing state and a non-empty,
active steady state. We find numerically that this transition belongs to the
same universality class as BAW's with an even number of offspring, $n\geq 4$,
and that of other models whose dynamic rules conserve the parity of the
particles locally. The simplicity of the model is exploited in computer
simulations to obtain various critical exponents with a high level of accuracy.
