  Feder and Vardi studied Schaefer’s dichotomy and conjectured that it holds for all finite-domain Constraint Satisfaction Problems (CSP) [Feder and Vardi, 1999]. A finite-domain CSP, C, consists of a finite domain, D, and a finite set of relations \(R_1, \ldots , R_k\) over D.  An instance of C consists of a set of variables, \(v_1, \ldots v_n\) and a conjunction of atoms \(\varphi  \equiv \bigwedge R_i(v_{j_1}, \ldots)\). The answer to the instance, \(\varphi\), is “yes”, i.e., \(\varphi \in C\) iff there is an assignment of the variables to elements of the domain, D, so that \(\varphi\) is satisfied. 