Position Paper: Formal Methods in Agile Development

Modern software development must be agile. It has to accept that soft- ware systems undergo a lot of changes due to changes in the application context (for example changing conditions on the markets and changes due to the jurisdiction) and base technology (e.g. integration of new frameworks or updates of the platform) in their life cycle. Thus, most of the activities in the development process are redesign steps. Even requirements are not stable. They change in time as the context of the system changes. There is no time for complex correctness proofs of the implementation with respect to the requirements. Automatic (regression) testing has proved to be sufficient for correct system behaviour. Therefore the agile developer does not learn and apply formal methods himself. In order to be agile, however, he relies on tools for automatic refactoring of the system or of certain parts of it. These tools are able to change the system structure without changing its behaviour. We argue in this paper that, in order to build such tools, further research in the area of formal system modelling and development is needed

Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders

Convolutional autoencoders have emerged as popular methods for unsupervised defect segmentation on image data. Most commonly, this task is performed by thresholding a pixel-wise reconstruction error based on an $\ell^p$ distance. This procedure, however, leads to large residuals whenever the reconstruction encompasses slight localization inaccuracies around edges. It also fails to reveal defective regions that have been visually altered when intensity values stay roughly consistent. We show that these problems prevent these approaches from being applied to complex real-world scenarios and that it cannot be easily avoided by employing more elaborate architectures such as variational or feature matching autoencoders. We propose to use a perceptual loss function based on structural similarity which examines inter-dependencies between local image regions, taking into account luminance, contrast and structural information, instead of simply comparing single pixel values. It achieves significant performance gains on a challenging real-world dataset of nanofibrous materials and a novel dataset of two woven fabrics over the state of the art approaches for unsupervised defect segmentation that use pixel-wise reconstruction error metrics

On Single-Pushout Rewriting of Partial Algebras

We introduce Single-Pushout Rewriting for arbitrary partial algebras. Thus, we give up the usual restriction to graph structures, which are algebraic categories with unary operators only. By this generalisation, we obtain an integrated and straightforward treatment of graphical structures (objects) and attributes (data). We lose co-completeness of the underlying category. Therefore, a rule is no longer applicable at any match. We characterise the new application condition and make constructive use of it in some practical examples

Refactoring Informations Systems

We present our formal framework for the refactoring of complete information systems, i.e., the data model and the data itself. It is described using general and abstract notions of category theory and can handle addition, renaming and removal of model objects as well as folding and unfolding within complete and partial object compositions

Impact of High Electric Fields on the Behavior of Water Droplets under Various Ambient Conditions: Experiments and Theory

The interaction of water droplets and electric fields is present in various applications like electrowetting, electrostatic lenses or high-voltage composite insulators. Depending on the application, the electric field is used to actively control the behaviour of the liquid as for example for electrostatic lenses, or is only considered as a boundary condition which has a negative influence on, as for instance, the properties of high-voltage composite insulators. The understanding of the underlying physical mechanisms is essential to predict and control the behaviour of liquids under the impact of electric fields. Even though the general behaviour of water under the impact of constant, alternating and transient electric fields was already investigated experimentally, theoretical and numerically in the past, the influence of electric charges on the behaviour of water droplets or the interaction of nearby droplets under the impact of transient electric fields are still not completely clear. It is well known that water droplets are significantly influenced by external electric fields, resulting in oscillations or deformations. Hence, the presence of electric fields might indirectly impact other physical mechanism like ice nucleation, which is controversially discussed and not unambiguously proven. The present work aims to expand the knowledge of the impact of electric fields on sessile droplets under various ambient conditions. Therefore, the influence of electric charges on the motion of single droplets and the inception field strength for electrical partial discharges for single and multiple droplets are experimentally investigated depending on the electric field strength, droplet volume as well as frequency of the electric field. The oscillation behaviour and partial discharge inception of water droplets are significantly influenced by electric charges. In addition, the interaction of nearby droplets under the impact of transient electric fields is determined and the behaviour is categorized depending on the influencing factors. Furthermore, it is confirmed that heterogeneous ice nucleation can be clearly promoted by the presence of electric fields. While constant electric fields have an almost negligible influence, alternating and transient electric fields significantly promote ice nucleation depending on the frequency, type and strength of the electric field. This present experimental work expands the understanding of the impact of electric fields on water droplets under various boundary conditions and might help to improve and optimize applications like the operation of high-voltage composite insulators at ambient and cold conditions

Characterizing Van Kampen Squares via Descent Data

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

On the essence of parallel independence for the double-pushout and sesqui-pushout approaches

Parallel independence between transformation steps is a basic notion in the algebraic approaches to graph transformation, which is at the core of some static analysis techniques like Critical Pair Analysis. We propose a new categorical condition of parallel independence and show its equivalence with two other conditions proposed in the literature, for both left-linear and non-left-linear rules. Next we present some preliminary experimental results aimed at comparing the three conditions with respect to computational efficiency. To this aim, we implemented the three conditions, for left-linear rules only, in the Verigraph system, and used them to check parallel independence of pairs of overlapping redexes generated from some sample graph transformation systems over categories of typed graphs