Ranking Templates for Linear Loops

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 $\exists\forall$-constraint into an $\exists$-constraint.Comment: TACAS 201

Alternativa, Separazione e Problemi di Classificazione

Nella prima parte di questa tesi vengono presentati i principali teoremi di alternativa e di separazione. Viene quindi mostrato che si tratta di linguaggi diversi per esprimere le stesse proprietà strutturali. Nella seconda parte della tesi si prendono invec in considerazione i problemi di classificazione. Dopo aver spiegato di cosa si tratta, si mostrano le connessioni tra i teoremi precedentemente studiati e le applicazioni pratiche. Infine viene fatta una panoramica dei metodi di classificazione più usati

Ranking Templates for Linear Loops

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 lexicographic 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 $\exists\forall$-constraint into an $\exists$-constraint