On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System

Miki Hermann 1 Laurent Juban 1 Phokion G. Kolaitis 2
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We investigate the computational complexity of counting the Hilbert basis of a homogeneous system of linear Diophantine equations. We establish lower and upper bound on the complexity of this problem by showing that counting the Hilbert basis is #P-hard and belongs to the class #NP. Moreover, we investigate the complexity of variants obtained by restricting the number of occurrences of the variables in the system.
Type de document :
Rapport
[Intern report] 98-R-281 || hermann98c, 1998, 16 p
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https://hal.inria.fr/inria-00098565
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Soumis le : lundi 25 septembre 2006 - 17:03:30
Dernière modification le : jeudi 11 janvier 2018 - 06:19:58

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  • HAL Id : inria-00098565, version 1

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Miki Hermann, Laurent Juban, Phokion G. Kolaitis. On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System. [Intern report] 98-R-281 || hermann98c, 1998, 16 p. 〈inria-00098565〉

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