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Linear Ranking for Linear Lasso Programs

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Automated Technology for Verification and Analysis

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8172))

Abstract

The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and an invariant. We present the—to the best of our knowledge—first method to synthesize termination arguments for lasso programs that uses linear arithmetic.We prove a completeness theorem. The completeness theorem establishes that, even though we use only linear (as opposed to non-linear) constraint solving, we are able to compute termination arguments in several interesting cases. The key to our method lies in a constraint transformation that replaces a disjunction by a sum.

This work is supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR14 AVACS).

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Authors and Affiliations

  1. University of Freiburg, Germany

    Matthias Heizmann, Jochen Hoenicke, Jan Leike & Andreas Podelski

Authors
  1. Matthias Heizmann
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  2. Jochen Hoenicke
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  3. Jan Leike
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  4. Andreas Podelski
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Editor information

Editors and Affiliations

  1. University of Engineering and Technology, Vietnam National University, Xuan Thuy Street, 144, Hanoi, Vietnam

    Dang Van Hung

  2. School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Mizuhito Ogawa

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Heizmann, M., Hoenicke, J., Leike, J., Podelski, A. (2013). Linear Ranking for Linear Lasso Programs. In: Van Hung, D., Ogawa, M. (eds) Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, vol 8172. Springer, Cham. https://doi.org/10.1007/978-3-319-02444-8_26

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  • DOI: https://doi.org/10.1007/978-3-319-02444-8_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02443-1

  • Online ISBN: 978-3-319-02444-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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