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.

Polynomial constraint solving over finite domains with the modified Bernstein form / Bergenti, Federico; Monica, Stefania; Rossi, Gianfranco. - ELETTRONICO. - 1645:(2016), pp. 118-131. ((Intervento presentato al convegno 31st Italian Conference on Computational Logic (CILC 2016) tenutosi a Milano nel 2016.

### Polynomial constraint solving over finite domains with the modified Bernstein form

#### Abstract

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.
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2016
Polynomial constraint solving over finite domains with the modified Bernstein form / Bergenti, Federico; Monica, Stefania; Rossi, Gianfranco. - ELETTRONICO. - 1645:(2016), pp. 118-131. ((Intervento presentato al convegno 31st Italian Conference on Computational Logic (CILC 2016) tenutosi a Milano nel 2016.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11381/2818449`
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