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International Colloquium on Theoretical Aspects of Computing

ICTAC 2017: Theoretical Aspects of Computing – ICTAC 2017 pp 213–228Cite as

Constructing Cycles in the Simplex Method for DPLL(T)

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10580))

Abstract

Modern SMT solvers use a special DPLL(T) variant of the simplex algorithm to solve satisfiability problems in linear real arithmetic. Termination is guaranteed by Bland’s pivot selection rule, but it is not immediately obvious that such a rule is required. For the traditional simplex method non-termination is well-understood, but the cycling examples from the literature do not immediately carry over to the DPLL(T) variant. We present two SMT encodings of the problem of finding cycles, using linear and nonlinear real arithmetic.

This research was supported by Austrian Science Fund (FWF) project P27528.

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Notes

  1. 1.

    http://cl-informatik.uibk.ac.at/research/simplex/

  2. 2.

    We use \(\max (|p|,|q|)\) as a measure of simplicity of a rational number p / q; the smaller the measure the simpler the number.

  3. 3.

    While CVC4 [3] (snapshot version 2017-06-14) also has support for NRA, it cannot produce models, making it unfit for our purposes.

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Acknowledgements

We thank the reviewers for their constructive feedback.

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Authors and Affiliations

  1. Department of Computer Science, University of Innsbruck, Innsbruck, Austria

    Bertram Felgenhauer & Aart Middeldorp

Authors
  1. Bertram Felgenhauer
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  2. Aart Middeldorp
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Correspondence to Bertram Felgenhauer .

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Editors and Affiliations

  1. Vietnam National University, Hanoi, Vietnam

    Dang Van Hung

  2. University of New Mexico, Albuquerque, New Mexico, USA

    Deepak Kapur

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Felgenhauer, B., Middeldorp, A. (2017). Constructing Cycles in the Simplex Method for DPLL(T). In: Hung, D., Kapur, D. (eds) Theoretical Aspects of Computing – ICTAC 2017. ICTAC 2017. Lecture Notes in Computer Science(), vol 10580. Springer, Cham. https://doi.org/10.1007/978-3-319-67729-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-67729-3_13

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