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Conference of the Italian Association for Artificial Intelligence

AI*IA 2016: AI*IA 2016 Advances in Artificial Intelligence pp 179–191Cite as

A Subdivision Approach to the Solution of Polynomial Constraints over Finite Domains Using the Modified Bernstein Form

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10037))

Abstract

This paper discusses an algorithm to solve polynomial constraints over finite domains, namely constraints which are expressed in terms of equalities, inequalities and disequalities of polynomials with integer coefficients whose variables are associated with finite domains. The proposed algorithm starts with a preliminary step intended to rewrite all constraints to a canonical form. Then, the modified Bernstein form of obtained polynomials is used to recursively restrict the domains of variables, which are assumed to be initially approximated by a bounding box. The proposed algorithm proceeds by subdivisions, and it ensures that each variable is eventually associated with the inclusion-maximal finite domain in which the set of constraints is satisfiable. If arbitrary precision integer arithmetic is available, no approximation is introduced in the solving process because the coefficients of the modified Bernstein form are integer numbers.

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References

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43124, Parma, Italy

    Federico Bergenti, Stefania Monica & Gianfranco Rossi

Authors
  1. Federico Bergenti
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  2. Stefania Monica
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  3. Gianfranco Rossi
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Corresponding author

Correspondence to Federico Bergenti .

Editor information

Editors and Affiliations

  1. University of Genoa , Genova, Italy

    Giovanni Adorni

  2. University of Parma , Parma, Italy

    Stefano Cagnoni

  3. University of Siena , Siena, Italy

    Marco Gori

  4. University of Genova , Genova, Italy

    Marco Maratea

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Bergenti, F., Monica, S., Rossi, G. (2016). A Subdivision Approach to the Solution of Polynomial Constraints over Finite Domains Using the Modified Bernstein Form. In: Adorni, G., Cagnoni, S., Gori, M., Maratea, M. (eds) AI*IA 2016 Advances in Artificial Intelligence. AI*IA 2016. Lecture Notes in Computer Science(), vol 10037. Springer, Cham. https://doi.org/10.1007/978-3-319-49130-1_14

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  • DOI: https://doi.org/10.1007/978-3-319-49130-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49129-5

  • Online ISBN: 978-3-319-49130-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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