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

  title={On the Complexity of Counting the Hilbert Basis of a Linear Diophnatine System},
  author={Miki Hermann and Laurent Juban and Phokion G. Kolaitis},
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. 
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