Parallel computation for well-endowed rings and space-bounded probabilistic machines
Information and Control
The structure of polynomial ideals and Grobner bases
SIAM Journal on Computing
The membership problem for unmixed polynomial ideals is solvable in single exponential time
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
Exponential space computation of Gröbner bases
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Computational Commutative Algebra 1
Computational Commutative Algebra 1
Degree bounds for Gröbner bases of low-dimensional polynomial ideals
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Approaches to modeling business processes: a critical analysis of BPMN, workflow patterns and YAWL
Software and Systems Modeling (SoSyM)
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The computation of a Gröbner basis of a polynomial ideal is known to be exponential space complete. We revisit the algorithm by Kühnle and Mayr using recent improvements of various degree bounds. The result is an algorithm which is exponential in the ideal dimension (rather than the number of indeterminates). Furthermore, we provide an incremental version of the algorithm which is independent of the knowledge of degree bounds. Employing a space-efficient implementation of Buchberger's S-criterion, the algorithm can be implemented such that the space requirement depends on the representation and Gröbner basis degrees of the problem instance (instead of the worst case) and thus is much lower in average.