Linear Ranking for Linear Lasso Programs

  • Matthias Heizmann
  • Jochen Hoenicke
  • Jan Leike
  • Andreas Podelski
Conference paper

DOI: 10.1007/978-3-319-02444-8_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8172)
Cite this paper as:
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. ATVA 2013. Lecture Notes in Computer Science, vol 8172. Springer, Cham

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.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Matthias Heizmann
    • 1
  • Jochen Hoenicke
    • 1
  • Jan Leike
    • 1
  • Andreas Podelski
    • 1
  1. 1.University of FreiburgGermany

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