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

  • Miki Hermann
  • Laurent Juban
  • Phokion G. Kolaitis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1705)

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.

Keywords

Bipartite Graph Minimal Solution Truth Assignment Disjunctive Normal Form Satisfying Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Miki Hermann
    • 1
  • Laurent Juban
    • 1
  • Phokion G. Kolaitis
    • 2
  1. 1.LORIA (CNRS and Université Henri Poincaré Nancy 1)Vandœuvre-lès-NancyFrance
  2. 2.Computer Science DepartmentUniversity of CaliforniaSanta CruzUSA

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