  We determine all families of Markovian three-states lattice gases with pair
interaction and a single local conservation law. One such family of models is
an asymmetric exclusion process where particles exist in two different
nonconserved states. We derive conditions on the transition rates between the
two states such that the shock has a particularly simple structure with minimal
intrinsic shock width and random walk dynamics. We calculate the drift velocity
and diffusion coefficient of the shock.
