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 obtained by restricting the number of occurrences of the variables in the system.
Last modified: Tue Jul 20 12:23:12 MET DST 1999