Infinite-state graph transformation systems under adverse conditions

We present an approach for modeling adverse conditions by graph transformation systems. To this end, we introduce joint graph transformation systems which involve a system, an interfering environment, and an automaton modeling their interaction. For joint graph transformation systems, we present notions of correctness under adverse conditions. Some instances of correctness are expressible in LTL (linear temporal logic), or in CTL (computation tree logic), respectively. In these cases, verification of joint graph transformation systems is reduced to temporal model checking. To handle infinite state spaces, we incorporate the concept of well-structuredness. We discuss ideas for the verification of joint graph transformation systems using results based on well-structuredness.

A tale of two graph models: a case study in wireless sensor networks

Designing and reasoning about complex systems such as wireless sensor networks is hard due to highly dynamic environments: sensors are heterogeneous, battery-powered, and mobile. While formal modelling can provide rigorous mechanisms for design/reasoning, they are often viewed as difficult to use. Graph rewrite-based modelling techniques increase usability by providing an intuitive, flexible, and diagrammatic form of modelling in which graph-like structures express relationships between entities while rewriting mechanisms allow model evolution. Two major graph-based formalisms are Graph Transformation Systems (GTS) and Bigraphical Reactive Systems (BRS). While both use similar underlying structures, how they are employed in modelling is quite different. To gain a deeper understanding of GTS and BRS, and to guide future modelling, theory, and tool development, in this experience report we compare the practical modelling abilities and style of GTS and BRS when applied to topology control in WSNs. To show the value of the models, we describe how analysis may be performed in both formalisms. A comparison of the approaches shows that although the two formalisms are different, from both a theoretical and practical modelling standpoint, they are each successful in modelling topology control in WSNs. We found that GTS, while featuring a small set of entities and transformation rules, relied on entity attributes, rule application based on attribute/variable side-conditions, and imperative control flow units. BRS on the other hand, required a larger number of entities in order to both encode attributes directly in the model (via nesting) and provide tagging functionality that, when coupled with rule priorities, implements control flow. There remains promising research mapping techniques between the formalisms to further enable flexible and expressive modelling.

Comprehensive Systems: A formal foundation for Multi-Model Consistency Management

Model management is a central activity in Software Engineering. The most challenging aspect of model management is to keep inter-related models consistent with each other while they evolve. As a consequence, there is a lot of scientific activity in this area, which has produced an extensive body of knowledge, methods, results and tools. The majority of these approaches, however, are limited to binary inter-model relations; i.e. the synchronisation of exactly two models. Yet, not every multi-ary relation can be factored into a family of binary relations. In this paper, we propose and investigate a novel comprehensive system construction, which is able to represent multi-ary relations among multiple models in an integrated manner and thus serves as a formal foundation for artefacts used in consistency management activities involving multiple models. The construction is based on the definition of partial commonalities among a set of models using the same language, which is used to denote the (local) models. The main theoretical results of this paper are proofs of the facts that comprehensive systems are an admissible environment for (i) applying formal means of consistency verification (diagrammatic predicate framework), (ii) performing algebraic graph transformation (weak adhesive HLR category), and (iii) that they generalise the underlying setting of graph diagrams and triple graph grammars.

Formal testing of timed graph transformation systems using metric temporal graph logic

Embedded real-time systems generate state sequences where time elapses between state changes. Ensuring that such systems adhere to a provided specification of admissible or desired behavior is essential. Formal model-based testing is often a suitable cost-effective approach. We introduce an extended version of the formalism of symbolic graphs, which encompasses types as well as attributes, for representing states of dynamic systems. Relying on this extension of symbolic graphs, we present a novel formalism of timed graph transformation systems (TGTSs) that supports the model-based development of dynamic real-time systems at an abstract level where possible state changes and delays are specified by graph transformation rules. We then introduce an extended form of the metric temporal graph logic (MTGL) with increased expressiveness to improve the applicability of MTGL for the specification of timed graph sequences generated by a TGTS. Based on the metric temporal operators of MTGL and its built-in graph binding mechanics, we express properties on the structure and attributes of graphs as well as on the occurrence of graphs over time that are related by their inner structure. We provide formal support for checking whether a single generated timed graph sequence adheres to a provided MTGL specification. Relying on this logical foundation, we develop a testing framework for TGTSs that are specified using MTGL. Lastly, we apply this testing framework to a running example by using our prototypical implementation in the tool AutoGraph.