  The most general exclusion single species reaction-diffusion models with
nearest-neighbor interactions one a one dimensional lattice are investigated,
for which the evolution of full intervals are closed. Using a generating
function method, the probability that n consecutive sites be full is
investigated. The stationary values of these probabilities, as well as the
spectrum of the time translation generator (Hamiltonian) of these are obtained.
It is shown that depending on the reaction rates the model could exhibit a
dynamical phase transition.
