  We conjecture that for a wide class of interacting particle systems evolving
in discrete time, namely conservative cellular automata with piecewise linear
flow diagram, relaxation to the limit set follows the same power law at
critical points. We further describe the structure of the limit sets of such
systems as unions of shifts of finite type. Relaxation to the equilibrium
resembles ballistic annihilation, with ``defects'' propagating in opposite
direction annihilating upon collision.
