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Standard forms for rational linear arithmetic in constraint logic programming

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Abstract

Rational (resp. real) linear arithmetic is a computation domain included in several constraint logic programming languages. The decision procedure for this computation domain is usually based on a standard form for the representation of constraints. In this paper we show that the standard form used by the simplex algorithm for the representation of equations is not appropriate for deciding systems of linear constraints including disequations. We propose a new standard form, derived from it which overcomes the difficulty. We then show that the simplex algorithm can be extended to preserve this standard form through pivoting. These results provide the basis for an efficient and incremental procedure for rational linear arithmetic inside constraint logic programming languages.

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Authors and Affiliations

  1. Brown University, Box 1910, 02912, Providence, RI, USA

    Pascal Van Hentenryck

  2. Postfach 41, A-1191, Wien, Austria

    Thomas Graf

Authors
  1. Pascal Van Hentenryck
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  2. Thomas Graf
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Additional information

This paper is a revised and extended version of [19]. Part of this work was done while the authors were at ECRC, Munich (Germany).

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Van Hentenryck, P., Graf, T. Standard forms for rational linear arithmetic in constraint logic programming. Ann Math Artif Intell 5, 303–319 (1992). https://doi.org/10.1007/BF01543480

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