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

  • Authors:

  • Miki Hermann;Laurent Juban;Phokion G. Kolaitis

  • Affiliations:

  • -;-;-

  • Venue:
  • LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
  • Year:
  • 1999

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Abstract

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.