Minkowski addition of polytopes: computational complexity and applications to Gro¨bner bases
SIAM Journal on Discrete Mathematics
A New Criterion for Normal Form Algorithms
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Generalized normal forms and polynomial system solving
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Stable normal forms for polynomial system solving
Theoretical Computer Science
Complexity of Gröbner basis detection and border basis detection
Theoretical Computer Science
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Border basis detection (BBD) is described as follows: given a set of generators of an ideal, decide whether that set of generators is a border basis of the ideal with respect to some order ideal. The motivation for this problem comes from a similar problem related to Grobner bases termed as Grobner basis detection (GBD) which was proposed by Gritzmann and Sturmfels (1993). GBD was shown to be NP-hard by Sturmfels and Wiegelmann (1996). In this paper, we investigate the computational complexity of BBD and show that it is NP-complete.