This paper introduces an instantiation of the constraint logic programming scheme called CLP(PolyFD) in which variables take values from finite subsets of the integers and constraints are expressed as equalities, inequalities, and disequalities of polynomials with integer coefficients. Such constraints, which we call polynomial constraints over finite domains, can be treated effectively by means of a specific solver under the assumption that initial approximations of the domains of variables are available. The proposed solver deals with constraints in a canonical form and it uses the modified Bernstein form of polynomials to detect the satisfiability of constraints. The solver is complete and a preliminary assessment of its performance is reported.
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