Abstract
The Border Basis Algorithm (BBA) still suffers from the lack of analogues of Buchberger’s criteria for avoiding unnecessary reductions. In this paper we develop a signature based technique which provides a first remedial step: signature bounds allow us to recognize multiple reductions of the same ancestor polynomial. The new signature based algorithm is then combined with the Boolean BBA for ideals of Boolean polynomials. Experiments show that it is at least 5 times faster than the standard Boolean BBA.
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Acknowledgements
The authors thank Jan Burchard for valuable input about SAT solvers and Michael Brickenstein and Alexander Dreyer for providing us with a better insight into the structure of PolyBoRi. This work was financially supported by the DFG Project “Algebraische Fehlerangriffe” [KR 1907/6-2].
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Horáček, J., Kreuzer, M. & Messeng Ekossono, AS. A Signature Based Border Basis Algorithm. Math.Comput.Sci. 14, 177–189 (2020). https://doi.org/10.1007/s11786-020-00459-z
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DOI: https://doi.org/10.1007/s11786-020-00459-z