  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 $E_n(t)$'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.
