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On Fourier's algorithm for linear arithmetic constraints

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Abstract

In the 1820s Fourier provided the first algorithm for solving linear arithmetic constraints. In other words, this algorithm determines whether or not the polyhedral set associated with the constraints is empty. We show here that Fourier's algorithm has an important hidden property: in effect it also computes the affine hull of the polyhedral set. This result is established by making use of a recent theorem on the independence of negative constraints.

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, P.O. Box 704, 10598, Yorktown Heights, NY, USA

    Jean-Louis Lassez & Michael J. Maher

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  1. Jean-Louis Lassez
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  2. Michael J. Maher
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Lassez, JL., Maher, M.J. On Fourier's algorithm for linear arithmetic constraints. Journal of Automated Reasoning 9, 373–379 (1992). https://doi.org/10.1007/BF00245296

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  • DOI: https://doi.org/10.1007/BF00245296

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