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

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Book cover Logic for Programming and Automated Reasoning (LPAR 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,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.

Research partially supported by NSF grants CCR-9610257 and CCR-9732041.

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Author information

Authors and Affiliations

  1. LORIA (CNRS and Université Henri Poincaré Nancy 1), BP 239, 54506, Vandœuvre-lès-Nancy, France

    Miki Hermann & Laurent Juban

  2. Computer Science Department, University of California, Santa Cruz, CA, 95064, USA

    Phokion G. Kolaitis

Authors
  1. Miki Hermann
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  2. Laurent Juban
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  3. Phokion G. Kolaitis
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Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Harald Ganzinger

  2. AT&T Labs Research, 180 Park Ave, Florham Park, NJ, 07932-0971, USA

    David McAllester

  3. Department of Computer Science, University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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© 1999 Springer-Verlag Berlin Heidelberg

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Hermann, M., Juban, L., Kolaitis, P.G. (1999). On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 1999. Lecture Notes in Computer Science(), vol 1705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48242-3_2

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  • DOI: https://doi.org/10.1007/3-540-48242-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66492-5

  • Online ISBN: 978-3-540-48242-0

  • eBook Packages: Springer Book Archive

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