  Constraint Satisfaction Problems (CSP) constitute a convenient way to capture
many combinatorial problems. The general CSP is known to be NP-complete, but
its complexity depends on a template, usually a set of relations, upon which
they are constructed. Following this template, there exist tractable and
intractable instances of CSPs. It has been proved that for each CSP problem
over a given set of relations there exists a corresponding CSP problem over
graphs of unary functions belonging to the same complexity class. In this short
note we show a dichotomy theorem for every finite domain D of CSP built upon
graphs of homogeneous co-Boolean functions, i.e., unary functions sharing the
Boolean range {0, 1}.
