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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Ranking Templates for Linear Loops
verfasst von : Jan Leike, Matthias Heizmann
Erschienen in: Tools and Algorithms for the Construction and Analysis of Systems
Verlag: Springer Berlin Heidelberg
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We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on
linear ranking templates
. Linear ranking templates are parametrized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. This approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, piecewise, and lexicographic ranking functions. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin’s Transposition Theorem instead of Farkas Lemma to transform the generated ∃ ∀-constraint into an ∃-constraint.