Exactly solvable models through the empty interval method, for more-than-two-site interactions

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in which more than two neighbouring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E-n(t), 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-neighbour interaction is studied.