Jan Stückrath

On the Decidability Status of Reachability and Coverability in Graph Transformation Systems

We study decidability issues for reachability problems in graph transformation systems, a powerful infinite-state model. For a fixed initial configuration, we consider reachability of an entirely specified configuration and of a configuration that satisfies a given pattern (coverability). The former is a fundamental problem for any computational model, the latter is strictly related to verification of safety properties in which the pattern specifies an infinite set of bad configurations. In this paper we reformulate results obtained, e.g., for context-free graph grammars and concurrency models, such as Petri nets, in the more general setting of graph transformation systems and study new results for classes of models obtained by adding constraints on the form of reduction rules.

A General Framework for Well-Structured Graph Transformation Systems

Graph transformation systems (GTSs) can be seen as well-structured transition systems (WSTSs), thus obtaining decidability results for certain classes of GTSs. In earlier work it was shown that well-structuredness can be obtained using the minor ordering as a well-quasi-order. In this paper we extend this idea to obtain a general framework in which several types of GTSs can be seen as (restricted) WSTSs. We instantiate this framework with the subgraph ordering and the induced subgraph ordering and apply it to analyse a simple access rights management system.

Uncover: Using Coverability Analysis for Verifying Graph Transformation Systems

Uncover is a tool for high level verification of distributed or concurrent systems. It uses graphs and graph transformation rules to model these systems in a natural way. Errors in such a system are modelled by upward-closed sets for which two orders are provided, the subgraph and the minor ordering. We can then exploit the theory of well-structured transition systems to obtain exact or approximating decidability results (depending on the order and system) for the question whether an error can occur or not. For this framework we also introduced an extension of classical graph transformation which is capable of modelling broadcast protocols.

Lattice-extended Coloured Petri Net Rewriting for Adaptable User Interface Models

Adaptable user interfaces (UI) have shown a great variety of advantages in human computer interaction compared to classic UI designs. We show how adaptable UIs can be built by introducing coloured Petri nets to connect the UI’s physical representation with the system to be controlled. UI development benefits from formal modelling approaches regarding the derived close integration of creation, execution, and reconfiguration of formal UI models. Thus, adaptation does not only change the physical representation, but also the connecting Petri net. For the latter transformation, we enhance the DPO rewriting formalism by using an order on the set of labels and softening the label-preserving property of morphisms, i.e., an element can also be mapped to another element if the label is larger. We use lattices to ensure correctness and state application conditions of rewriting steps. Finally we define an order compatible with our framework for the use in our implementation.

Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations

We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be transformed by the rule as well. For the new class for graph rewrite rules, we provide a symbolic procedure working on minimal representations of upward closed sets of configurations. We prove correctness and effectiveness of the procedure by a categorical presentation of rewrite rules as well as the involved order, and using results for well-structured transition systems. We apply the resulting procedure to the analysis of the Distributed Dining Philosophers protocol on an arbitrary network structure.

Well-structured graph transformation systems

Graph transformation systems (GTSs) can be seen as well-structured transition systems (WSTSs) and via well-structuredness it is possible to obtain decidability results for certain classes of GTSs. We present a generic framework, parameterized over the well-quasi-order (wqo), in which several types of GTSs can be seen as (restricted) WSTSs. We instantiate this framework with three orders: the minor ordering, the subgraph ordering and the induced subgraph ordering. Furthermore we consider two case studies where we apply the theory to analyze a leader election protocol and a simple access rights management system with our tool Uncover.