Ranking Templates for Linear Loops

Jan Leike, Matthias Heizmann, Erika Abraham
2015 Logical Methods in Computer Science  
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 parameterized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. Our approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, nested, piecewise, parallel, and
more » ... exicographic ranking functions. These ranking templates can be combined to form more powerful templates. 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.
doi:10.2168/lmcs-11(1:16)2015 fatcat:jw3cdne6pbbrldnkav2mp72d5u