Hyper-arc consistency of polynomial constraints over finite domains using the modified Bernstein form

  • Federico BergentiEmail author
  • Stefania Monica


This paper describes an algorithm to enforce hyper-arc consistency of polynomial constraints defined over finite domains. First, the paper describes the language of so called polynomial constraints over finite domains, and it introduces a canonical form for such constraints. Then, the canonical form is used to transform the problem of testing the satisfiability of a constraint in a box into the problem of studying the sign of a related polynomial function in the same box, a problem which is effectively solved by using the modified Bernstein form of polynomials. The modified Bernstein form of polynomials is briefly discussed, and the proposed hyper-arc consistency algorithm is finally detailed. The proposed algorithm is a subdivision procedure which, starting from an initial approximation of the domains of variables, removes values from domains to enforce hyper-arc consistency.


Modified Bernstein form Polynomial constraints over finite domains Hyper-arc consistency Constraint satisfaction problems 

Mathematics Subject Classification (2010)

68T01 68T27 68T99 


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© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche, Fisiche e InformaticheUniversità degli Studi di ParmaParmaItaly

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