  We propose a new and general method for deriving exact density functionals in
one dimension for lattice gases with finite-range pairwise interactions.
Corresponding continuum functionals are derived by applying a proper limiting
procedure. The method is based on a generalised Markov property, which allows
us to set up a rather transparent scheme that covers all previously known exact
functionals for one-dimensional lattice gas or fluid systems. Implications for
a systematic construction of approximate density functionals in higher
dimensions are pointed out.
