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There are ca. 8 million persons with diabetes mellitus living in Germany. A late sequelae of diabetes is the diabetic foot syndrome (DFS), the prevalence of which is greatly increasing. It comprises all alterations of the foot as a result of diabetic polyneuropathy as well as microvascular and macrovascular (peripheral arterial occlusive disease, PAOD) alterations. Many of the ca. 250,000 newly diagnosed diabetic foot ulcers per year become chronic wounds. Despite intensive efforts for prevention, early diagnosis and adequate wound care, ca. 13,000 persons with diabetes undergo major limb amputation in Germany every year. With consistent treatment in interdisciplinary centers and by exhausting all possible methods of wound treatment, pressure relief as well as arterial revascularization, the major amputation rate in patients with diabetic foot problems can be reduced by 80%. With a suitable strategy of prevention, the recurrence rate of foot ulcers would be reduced.In Deutschland leben ca. 8 Mio. Menschen mit Diabetes mellitus. Eine Spätfolge dieser Erkrankung ist das diabetische Fußsyndrom (DFS), dessen Prävalenz stark ansteigt. Es umfasst alle Veränderungen am Fuß als Folge der diabetischen Polyneuropathie sowie mikro- und makroangiopathischer (periphere arterielle Verschlusskrankheit, PAVK) Veränderungen. Jährlich entstehen ca. 250.000 neue diabetische Fußulzera. Diese werden oft zu chronischen Wunden. Trotz intensiver Bemühungen um Prävention, frühzeitige Diagnostik und stadiengerechte Wundbehandlung werden in Deutschland jährlich ca. 13.000 Majoramputationen bei Diabetikern durchgeführt. Bei konsequenter Therapie des DFS in interdisziplinären Zentren mit Ausschöpfung aller Möglichkeiten der Wundbehandlung, der Druckentlastung sowie einer arteriellen Revaskularisation kann die Majoramputationsrate um bis zu 80 % gesenkt werden. Durch eine geeignete Präventionsstrategie wäre die große Gefahr der Rezidivulzera geringer.

Parity games can be used to solve satisfiability, verification and controller synthesis problems. As part of an effort to better understand their nature, or the nature of the problems they solve, preorders on parity games have been studied. Defining these relations, and in particular proving their transitivity, has proven quite difficult on occasion. We propose a uniform way of lifting certain preorders on Kripke structures to parity games and study the resulting preorders. We explore their relation with parity game preorders from the literature and we study new relations. Finally, we investigate whether these preorders can also be obtained via modal characterisations of the preorders.

We show how edge-labelled graphs can be used to represent first-order logic formulae. This gives rise to recursively nested structures, in which each level of nesting corresponds to the negation of a set of existentials. The model is a direct generalisation of the negative application conditions used in graph rewriting, which count a single level of nesting and are thereby shown to correspond to the fragment ∃¬∃ of first-order logic. Vice versa, this generalisation may be used to strengthen the notion of application conditions. We then proceed to show how these nested models may be flattened to (sets of) plain graphs, by allowing some structure on the labels. The resulting formulae-as-graphs may form the basis of a unification of the theories of graph transformation and predicate transformation.

We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph passing between components, meaning that components may “learn‿ and “forget‿ subgraphs through communication with other components. Secondly, composition is no longer binary; instead, it can be repeated for an arbitrary number of components.

We present a new abstraction technique for the exploration of graph transformation systems with infinite state spaces. This technique is based on patterns, simple graphs describing structures of interest that should be preserved by the abstraction. Patterns are collected into pattern graphs, layered graphs that capture the hierarchical composition of smaller patterns into larger ones. Pattern graphs are then abstracted to a finite universe of pattern shapes by collapsing equivalent patterns. This paper shows how the application of production rules can be lifted to pattern shapes, resulting in an over-approximation of the original system behaviour and thus enabling verification on the abstract level.

A datatype-generic function is a family of functions indexed by (the structure of) a type. Examples include equality tests, maps and pretty printers. Property based testing tools like QuickCheck and Gast support the de¯nition of properties and test-data generators, and they check if a monomorphic property is satis¯ed by the test cases. Generic functions satisfy generic properties and this paper discusses specifying and testing such properties. It shows how generic properties and gener- ators can be expressed, and explains three bugs we found and corrected in the Generic Haskell library

Model checking is increasingly popular for hardware and, more recently, software verification. In this paper we describe two different approaches to extend the benefits of model checking to systems whose behavior is specified by graph transformation systems. One approach is to encode the graphs into the fixed state vectors and the transformation rules into guarded commands that modify these state vectors appropriately to enjoy all the benefits of the years of experience incorporated in existing model checking tools. The other approach is to simulate the graph production rules directly and build the state space directly from the resultant graphs and derivations. This avoids the preprocessing phase, and makes additional abstraction techniques available to handle symmetries and dynamic allocation. In this paper we compare these approaches on the basis of three case studies elaborated in both of them, and we evaluate the results. Our conclusion is that the first approach outperforms the second if the dynamic and/or symmetric nature of the problem under analysis is limited, while the second shows its superiority for inherently dynamic and symmetric problems.