We investigate the computational complexity of counting the Hilbert basis of a homogeneous system of linear Diophantine equations. We establish lower and upper bounds 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 obtciined by restricting the number of occurrences of the variables in the system.
CITATION STYLE
Hermann, M., Juban, L., & Kolaitis, P. G. (1999). On the complexity of counting the Hilbert basis of a linear Diophantine system. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1705 LNAI, pp. 13–32). Springer Verlag. https://doi.org/10.1007/3-540-48242-3_2
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