  In this work we study, on a finite and periodic lattice, a class of
one-dimensional (bimolecular and single-species) reaction-diffusion models
which cannot be mapped onto free-fermion models.
  We extend the conventional empty-interval method, also called
  {\it interparticle distribution function} (IPDF) method, by introducing a
string function, which is simply related to relevant physical quantities.
  As an illustration, we specifically consider a model which cannot be solved
directly by the conventional IPDF method and which can be viewed as a
generalization of the {\it voter} model and/or as an {\it epidemic} model. We
also consider the {\it reversible} diffusion-coagulation model with input of
particles and determine other reaction-diffusion models which can be mapped
onto the latter via suitable {\it similarity transformations}.
  Finally we study the problem of the propagation of a wave-front from an
inhomogeneous initial configuration and note that the mean-field scenario
predicted by Fisher's equation is not valid for the one-dimensional
(microscopic) models under consideration.
