  We provide finite-size scaling estimates for the dynamical critical exponent
of the even parity-conserving universality class of critical behavior through
exact numerical diagonalizations of the time evolution operator of an
even-parity-conserving contact process. Our data seem to indicate that upon the
introduction of a small diffusion rate in the process its critical behavior
crosses over to that of the directed percolation universality class. A brief
discussion of the many-sector decomposability of parity-conserving contact
processes is presented.
