  We use a boolean cellular automaton model to describe the diffusion limited
dynamics of the irreversible reaction A+A->A+S on a 1D lattice. We derive a set
of equations for the dynamics of the empty interval probabilities from which
explicit expressions for the particle concentration and the two-point
correlation can be obtained. It is shown that the long time dynamics is in
agreement with the off-lattice solution. The early time behavior, however,
predicts a slower decay of the concentration.
