Abstract
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.
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Bergenti, F., Monica, S. Hyper-arc consistency of polynomial constraints over finite domains using the modified Bernstein form. Ann Math Artif Intell 80, 131–151 (2017). https://doi.org/10.1007/s10472-017-9544-z
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DOI: https://doi.org/10.1007/s10472-017-9544-z
Keywords
- Modified Bernstein form
- Polynomial constraints over finite domains
- Hyper-arc consistency
- Constraint satisfaction problems