Polynomial Constraint Solving over Finite Domains with the Modified Bernstein Form

This paper describes an algorithm that can be used to effectively solve polynomial constraints over finite domains. Such constraints are expressed in terms of inequalities of polynomials with integer coefficients whose variables are assumed to be defined over proper finite domains. The proposed algorithm first reduces each constraint to a canonical form, i.e., a specific form of inequality, then it uses the modified Bernstein form of resulting polynomials to incrementally restrict the domains of variables. No approximation is involved in the solving process because the coefficients of the modified Bernstein form of the considered type of polynomials are always integer numbers.