Automated reasoning for attributed graph properties

Graphs are ubiquitous in computer science. Moreover, in various application fields, graphs are equipped with attributes to express additional information such as names of entities or weights of relationships. Due to the pervasiveness of attributed graphs, it is highly important to have the means to express properties on attributed graphs to strengthen modeling capabilities and to enable analysis. Firstly, we introduce a new logic of attributed graph properties, where the graph part and attribution part are neatly separated. The graph part is equivalent to first-order logic on graphs as introduced by Courcelle. It employs graph morphisms to allow the specification of complex graph patterns. The attribution part is added to this graph part by reverting to the symbolic approach to graph attribution, where attributes are represented symbolically by variables whose possible values are specified by a set of constraints making use of algebraic specifications. Secondly, we extend our refutationally complete tableau-based reasoning method as well as our symbolic model generation approach for graph properties to attributed graph properties. Due to the new logic mentioned above, neatly separating the graph and attribution parts, and the categorical constructions employed only on a more abstract level, we can leave the graph part of the algorithms seemingly unchanged. For the integration of the attribution part into the algorithms, we use an oracle, allowing for flexible adoption of different available SMT solvers in the actual implementation. Finally, our automated reasoning approach for attributed graph properties is implemented in the tool AutoGraph integrating in particular the SMT solver Z3 for the attribute part of the properties. We motivate and illustrate our work with a particular application scenario on graph database query validation.Peer ReviewedPostprint (author's final draft

Formal Foundations for Information-Preserving Model Synchronization Processes Based on Triple Graph Grammars

Zwischen verschiedenen Artefakten, die Informationen teilen, wieder Konsistenz herzustellen, nachdem eines von ihnen geändert wurde, ist ein wichtiges Problem, das in verschiedenen Bereichen der Informatik auftaucht. Mit dieser Dissertation legen wir eine Lösung für das grundlegende Modellsynchronisationsproblem vor. Bei diesem Problem ist ein Paar solcher Artefakte (Modelle) gegeben, von denen eines geändert wurde; Aufgabe ist die Wiederherstellung der Konsistenz. Tripelgraphgrammatiken (TGGs) sind ein etablierter und geeigneter Formalismus, um dieses und verwandte Probleme anzugehen. Da sie auf der algebraischen Theorie der Graphtransformation und dem (Double-)Pushout Zugang zu Ersetzungssystemen basieren, sind sie besonders geeignet, um Lösungen zu entwickeln, deren Eigenschaften formal bewiesen werden können. Doch obwohl TGG-basierte Ansätze etabliert sind, leiden viele von ihnen unter dem Problem des Informationsverlustes. Wenn ein Modell geändert wurde, können während eines Synchronisationsprozesses Informationen verloren gehen, die nur im zweiten Modell vorliegen. Das liegt daran, dass solche Synchronisationsprozesse darauf zurückfallen Konsistenz dadurch wiederherzustellen, dass sie das geänderte Modell (bzw. große Teile von ihm) neu übersetzen. Wir schlagen einen TGG-basierten Ansatz vor, der fortgeschrittene Features von TGGs unterstützt (Attribute und negative Constraints), durchgängig formalisiert ist, implementiert und inkrementell in dem Sinne ist, dass er den Informationsverlust im Vergleich mit vorherigen Ansätzen drastisch reduziert. Bisher gibt es keinen TGG-basierten Ansatz mit vergleichbaren Eigenschaften. Zentraler Beitrag dieser Dissertation ist es, diesen Ansatz formal auszuarbeiten und seine wesentlichen Eigenschaften, nämlich Korrektheit, Vollständigkeit und Termination, zu beweisen. Die entscheidende neue Idee unseres Ansatzes ist es, Reparaturregeln anzuwenden. Dies sind spezielle Regeln, die es erlauben, Änderungen an einem Modell direkt zu propagieren anstatt auf Neuübersetzung zurückzugreifen. Um diese Reparaturregeln erstellen und anwenden zu können, entwickeln wir grundlegende Beiträge zur Theorie der algebraischen Graphtransformation. Zunächst entwickeln wir eine neue Art der sequentiellen Komposition von Regeln. Im Gegensatz zur gewöhnlichen Komposition, die zu Regeln führt, die Elemente löschen und dann wieder neu erzeugen, können wir Regeln herleiten, die solche Elemente stattdessen bewahren. Technisch gesehen findet der Synchronisationsprozess, den wir entwickeln, außerdem in der Kategorie der partiellen Tripelgraphen statt und nicht in der der normalen Tripelgraphen. Daher müssen wir sicherstellen, dass die für Double-Pushout-Ersetzungssysteme ausgearbeitete Theorie immer noch gültig ist. Dazu entwickeln wir eine (kategorientheoretische) Konstruktion neuer Kategorien aus gegebenen und zeigen, dass (i) diese Konstruktion die Axiome erhält, die nötig sind, um die Theorie für Double-Pushout-Ersetzungssysteme zu entwickeln, und (ii) partielle Tripelgraphen als eine solche Kategorie konstruiert werden können. Zusammen ermöglichen diese beiden grundsätzlichen Beiträge es uns, unsere Lösung für das grundlegende Modellsynchronisationsproblem vollständig formal auszuarbeiten und ihre zentralen Eigenschaften zu beweisen.Restoring consistency between different information-sharing artifacts after one of them has been changed is an important problem that arises in several areas of computer science. In this thesis, we provide a solution to the basic model synchronization problem. There, a pair of such artifacts (models), one of which has been changed, is given and consistency shall be restored. Triple graph grammars (TGGs) are an established and suitable formalism to address this and related problems. Being based on the algebraic theory of graph transformation and (double-)pushout rewriting, they are especially suited to develop solutions whose properties can be formally proven. Despite being established, many TGG-based solutions do not satisfactorily deal with the problem of information loss. When one model is changed, in the process of restoring consistency such solutions may lose information that is only present in the second model because the synchronization process resorts to restoring consistency by re-translating (large parts of) the updated model. We introduce a TGG-based approach that supports advanced features of TGGs (attributes and negative constraints), is comprehensively formalized, implemented, and is incremental in the sense that it drastically reduces the amount of information loss compared to former approaches. Up to now, a TGG-based approach with these characteristics is not available. The central contribution of this thesis is to formally develop that approach and to prove its essential properties, namely correctness, completeness, and termination. The crucial new idea in our approach is the use of repair rules, which are special rules that allow one to directly propagate changes from one model to the other instead of resorting to re-translation. To be able to construct and apply these repair rules, we contribute more fundamentally to the theory of algebraic graph transformation. First, we develop a new kind of sequential rule composition. Whereas the conventional composition of rules leads to rules that delete and re-create elements, we can compute rules that preserve such elements instead. Furthermore, technically the setting in which the synchronization process we develop takes place is the category of partial triple graphs and not the one of ordinary triple graphs. Hence, we have to ensure that the elaborate theory of double-pushout rewriting still applies. Therefore, we develop a (category-theoretic) construction of new categories from given ones and show that (i) this construction preserves the axioms that are necessary to develop the theory of double-pushout rewriting and (ii) partial triple graphs can be constructed as such a category. Together, those two more fundamental contributions enable us to develop our solution to the basic model synchronization problem in a fully formal manner and to prove its central properties

Consistency-by-Construction Techniques for Software Models and Model Transformations

A model is consistent with given specifications (specs) if and only if all the specifications are held on the model, i.e., all the specs are true (correct) for the model. Constructing consistent models (e.g., programs or artifacts) is vital during software development, especially in Model-Driven Engineering (MDE), where models are employed throughout the life cycle of software development phases (analysis, design, implementation, and testing). Models are usually written using domain-specific modeling languages (DSMLs) and specified to describe a domain problem or a system from different perspectives and at several levels of abstraction. If a model conforms to the definition of its DSML (denoted usually by a meta-model and integrity constraints), the model is consistent. Model transformations are an essential technology for manipulating models, including, e.g., refactoring and code generation in a (semi)automated way. They are often supposed to have a well-defined behavior in the sense that their resulting models are consistent with regard to a set of constraints. Inconsistent models may affect their applicability and thus the automation becomes untrustworthy and error-prone. The consistency of the models and model transformation results contribute to the quality of the overall modeled system. Although MDE has significantly progressed and become an accepted best practice in many application domains such as automotive and aerospace, there are still several significant challenges that have to be tackled to realize the MDE vision in the industry. Challenges such as handling and resolving inconsistent models (e.g., incomplete models), enabling and enforcing model consistency/correctness during the construction, fostering the trust in and use of model transformations (e.g., by ensuring the resulting models are consistent), developing efficient (automated, standardized and reliable) domain-specific modeling tools, and dealing with large models are continually making the need for more research evident. In this thesis, we contribute four automated interactive techniques for ensuring the consistency of models and model transformation results during the construction process. The first two contributions construct consistent models of a given DSML in an automated and interactive way. The construction can start at a seed model being potentially inconsistent. Since enhancing a set of transformations to satisfy a set of constraints is a tedious and error-prone task and requires high skills related to the theoretical foundation, we present the other contributions. They ensure model consistency by enhancing the behavior of model transformations through automatically constructing application conditions. The resulting application conditions control the applicability of the transformations to respect a set of constraints. Moreover, we provide several optimizing strategies. Specifically, we present the following: First, we present a model repair technique for repairing models in an automated and interactive way. Our approach guides the modeler to repair the whole model by resolving all the cardinalities violations and thereby yields a desired, consistent model. Second, we introduce a model generation technique to efficiently generate large, consistent, and diverse models. Both techniques are DSML-agnostic, i.e., they can deal with any meta-models. We present meta-techniques to instantiate both approaches to a given DSML; namely, we develop meta-tools to generate the corresponding DSML tools (model repair and generation) for a given meta-model automatically. We present the soundness of our techniques and evaluate and discuss their features such as scalability. Third, we develop a tool based on a correct-by-construction technique for translating OCL constraints into semantically equivalent graph constraints and integrating them as guaranteeing application conditions into a transformation rule in a fully automated way. A constraint-guaranteeing application condition ensures that a rule applies successfully to a model if and only if the resulting model after the rule application satisfies the constraint. Fourth, we propose an optimizing-by-construction technique for application conditions for transformation rules that need to be constraint-preserving. A constraint-preserving application condition ensures that a rule applies successfully to a consistent model (w.r.t. the constraint) if and only if the resulting model after the rule application still satisfies the constraint. We show the soundness of our techniques, develop them as ready-to-use tools, evaluate the efficiency (complexity and performance) of both works, and assess the overall approach in general as well. All our four techniques are compliant with the Eclipse Modeling Framework (EMF), which is the realization of the OMG standard specification in practice. Thus, the interoperability and the interchangeability of the techniques are ensured. Our techniques not only improve the quality of the modeled system but also increase software productivity by providing meta-tools for generating the DSML tool supports and automating the tasks

Typed lambda-terms in categorical attributed graph transformation

This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed lambda-calculus with inductive types. In this paper we present solutions to cope with single pushout construction for the graph structure and the computations functions. As this rewrite system uses inductive types, the expressiveness of attribute computations is facilitated and appears more efficient than the one based on Sigma-algebras. Some examples showing the interest of our computation approach are described in this paper

Towards Highly Scalable Runtime Models with History

Advanced systems such as IoT comprise many heterogeneous, interconnected, and autonomous entities operating in often highly dynamic environments. Due to their large scale and complexity, large volumes of monitoring data are generated and need to be stored, retrieved, and mined in a time- and resource-efficient manner. Architectural self-adaptation automates the control, orchestration, and operation of such systems. This can only be achieved via sophisticated decision-making schemes supported by monitoring data that fully captures the system behavior and its history. Employing model-driven engineering techniques we propose a highly scalable, history-aware approach to store and retrieve monitoring data in form of enriched runtime models. We take advantage of rule-based adaptation where change events in the system trigger adaptation rules. We first present a scheme to incrementally check model queries in the form of temporal logic formulas which represent the conditions of adaptation rules against a runtime model with history. Then we enhance the model to retain only information that is temporally relevant to the queries, therefore reducing the accumulation of information to a required minimum. Finally, we demonstrate the feasibility and scalability of our approach via experiments on a simulated smart healthcare system employing a real-world medical guideline.Comment: 8 pages, 4 figures, 15th International Symposium on Software Engineering for Adaptive and Self-Managing Systems (SEAMS2020