  We study a model of stochastic deposition-evaporation with recombination, of
three species of dimers on a line. This model is a generalization of the model
recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf
70} 1033) to $q\ge 3$ states per site. It has an infinite number of constants
of motion, in addition to the infinity of conservation laws of the original
model which are encoded as the conservation of the irreducible string. We
determine the number of dynamically disconnected sectors and their sizes in
this model exactly. Using the additional symmetry we construct a class of exact
eigenvectors of the stochastic matrix. The autocorrelation function decays with
different powers of $t$ in different sectors. We find that the spatial
correlation function has an algebraic decay with exponent 3/2, in the sector
corresponding to the initial state in which all sites are in the same state.
The dynamical exponent is nontrivial in this sector, and we estimate it
numerically by exact diagonalization of the stochastic matrix for small sizes.
We find that in this case $z=2.39\pm0.05$.
