Single-species reaction-diffusion systems on a one-dimensional lattice are
considered, in them more than two neighboring sites interact. Constraints on
the interaction rates are obtained, that guarantee the closedness of the time
evolution equation for En(t)'s, the probability that n consecutive sites
are empty at time t. The general method of solving the time evolution
equation is discussed. As an example, a system with next-nearest-neighbor
interaction is studied.Comment: 19 pages, LaTeX2