A superexponential lower bound for Gro¨bner bases and church-Rosser Commutative Thue systems
Information and Control
Membership in polynomial ideals over Q is exponential space complete
Proceedings of the 6th Annual Symposium on Theoretical Aspects of Computer Science on STACS 89
Minkowski addition of polytopes: computational complexity and applications to Gro¨bner bases
SIAM Journal on Discrete Mathematics
Computing Gröbner bases by FGLM techniques in a non-commutative setting
Journal of Symbolic Computation - Special issue on applications of the Gröbner basis method
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A New Criterion for Normal Form Algorithms
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
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
Computational Commutative Algebra 1
Computational Commutative Algebra 1
Groebner bases computation in Boolean rings for symbolic model checking
MS '07 The 18th IASTED International Conference on Modelling and Simulation
A new incremental algorithm for computing Groebner bases
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Border basis detection is NP-complete
Proceedings of the 36th international symposium on Symbolic and algebraic computation
| Hi-index | 5.23 |
Grobner basis detection (GBD) is defined as follows: given a set of polynomials, decide whether there exists-and if ''yes'' find-a term order such that the set of polynomials is a Grobner basis. This problem was proposed by Gritzmann and Sturmfels (1993) [12] and it was shown to be NP-hard by Sturmfels and Wiegelmann. We investigate the computational complexity of this problem when the given set of polynomials are the generators of a zero-dimensional ideal. Further, we propose the Border basis detection (BBD) problem which is formulated as follows: given a set of generators of an ideal, decide whether the set of generators is a border basis of the ideal with respect to some order ideal. We analyse the complexity of this problem and prove it to be NP-complete.