DPO Transformation with Open Maps

In the framework of graph transformation systems with Negative Application Conditions (NACs) the classical notion of switch equivalence of derivations is extended to permutation equivalence, because there are intuitively equivalent derivations which are not switch-equivalent if NACs are considered. By definition, two derivations are permutation-equivalent, if they respect the NACs and disregarding the NACs they are switch equivalent. A direct analysis of permutation equivalence is very complex in general, thus we propose a much more efficient analysis technique. For this purpose, we construct a Place/Transition Petri net, called dependency net, which encodes the dependencies among rule applications of the derivation, including the inhibiting effects of the NACs. The analysis of permutation equivalence is important for analysing simulation runs within development environments for systems modelled by graph transformation. The application of the technique is demonstrated by a graph transformation system within the context of workflow modelling. We show the effectiveness of the approach by comparing the minimal costs of a direct analysis with the costs of the efficient analysis applied to a derivation of our example system.

Using graph transformations to specify the dynamics of distributed systems and networks, we require a precise understanding of concurrency. Negative application conditions (NACs) are an essential means for controlling the application of rules, extending our ability to model complex systems. A classical notion of concurrency in graph transformation is based on shift equivalence and its representation by canonical derivations, i.e., normal forms of the shift operation anticipating independent steps. These concepts are lifted to graph transformation systems with NACs and it is shown that canonical derivations exist for so-called incremental NACs.

A rich concurrent semantics has been developed along the years for graph transformation systems, often generalizing in non-trivial ways concepts and results fist introduced for Petri nets. Besides the theoretical elegance, the concurrent semantic has potential applications in verification, e.g. in partial order reduction or in the use of finite prefixes of the unfolding for model checking. In practice (graph) transformation systems are often equipped with Negative Application Conditions, that describe forbidden contexts for the application of a rule. The talk will summarize some recent results showing that if the NACs are sufficiently simple (“incremental”) the concurrent semantics lifts smoothly to systems with NACs, but the general case requires original definitions and intuitions. Joint work with Reiko Heckel, Frank Hermann, Susann Gottmann and Nico Nachtigall

Use Case (UC) quality impacts the overall quality and defect rate of a system, as they specify the expected behavior of an implementation. In a previous work, we have defined an approach for a step-by-step translation from UCs written in natural language to a formal description in terms of Graph Transformation (GT), where each step of the UC was translated to a transformation rule. This UC formalization enables the detection of several specification problems even before an actual implementation is produced, thus reducing development costs. In this paper, we extend our approach to handle UC evolution by defining evolution rules , which are described as higher-order rules, simultaneously changing the behavior of a set of transformation rules. We also support the use of negative application conditions (NAC) associated both to the transformation and evolution rules. Analysis of the interplay between the evolution rules and the rules describing UC steps shows the effects of an evolution and serves to identify potential impacts, even before the changes are actually carried out. Besides defining the theoretical foundations of UC evolution with NACs, we have implemented the evolution analysis technique in the Verigraph tool and used it to verify impacts in 3 different case studies. The results demonstrate the applicability and usefulness of our approach to help developers in the evolution process based on UCs.

In each graph-grammar approach it is defined how and under which conditions graph productions can be applied to a given graph in order to obtain a derived graph. The conditions under which productions can be applied are called application conditions. Although the generative power of most of the known general graph-grammar approaches is sufficient to generate any recursively enumerable set of graphs, it is often convenient to have specific application conditions for each production. Such application conditions, on the one hand, include context conditions like the existence or non-existence of nodes, edges, or certain subgraphs in the given graph as well as embedding restrictions concerning the morphisms from the left-hand side of the production to the given graph. In this paper, the concept of application conditions introduced by Ehrig and Habel is restricted to contextual conditions, especially negative ones. In addition to the general concept, we state local confluence and the Parallelism Theorem for derivations with application conditions. Finally we study context-free graph grammars with application conditions with respect to their generative power.

The notion of refactoring --transforming the source-code of an object-oriented program without changing its external behaviour-- has increased the need for a precise definition of refactorings and their properties. This paper introduces a graph representation of those aspects of the source code that should be preserved by a refactoring, and graph rewriting rules as a formal specification for the refactoring transformations themselves. To this aim, we use type graphs, forbidden subgraphs, embedding mechansims, negative application conditions and controlled graph rewriting. We show that it is feasible to reason about the effect of refactorings on object-oriented programs independently of the programming language being used. This is crucial for the next generation of refactoring tools.

Malaria is one of the leading causes of death and illness in sub-Saharan Africa. In order to make timely decisions for control and elimination of malaria, researchers, and clinicians need access to integrated consistent knowledge sources. These knowledge sources often rely on dynamic and constantly changing databases and ontologies. It is crucial to manage changes and ensure that these changes do not cause inconsistencies in the integrated knowledge source. To this end, we propose the use of a formal model using graph transformations to monitor and manage the changes in a coherent way while preserving the consistency of the integrated structure through classical verification. In this paper, we use an algorithmic approach to graph transformation, instead of the more classical algebraic approach, to express the evolution of the data and ontological structures. In this model, each transformation is the result of applying rules to the graph, where the left-hand side is used to select a subgraph and the right-hand side is a sequence of elementary actions to be performed. Strategies are used to define how transformation rules should be applied. This approach enables us to define a Hoare-like calculus that can be used to verify the transformations and manage the changes. In this paper, we demonstrate the feasibility and significance of the proposed method through different use cases in malaria surveillance.

We define a graph grammar called node-replacement graph grammar with path controlled embedding (nPCE grammars) which use a sequence of edges instead of the single edge to embed a newly replaced graph into the host graph, then show some relationships between two-dimensional "coordinate grammars" and nPCE grammars. We also suggest an extension of PCE grammars to describe "disconnected coordinate languages".

Using graph transformation as a formalism to specify access control has several advantages, from the intuition provided by the visual aspect to the precise semantics and the systematic verification of constraints. Graph Transformations provide a uniform and precise framework for the specification of access control policies. After reviewing the basic notations of graph transformation, this article presents specification formalisms for workflow delegation policies using graph transformation. The authorization states are represented by graphs and state transition by graph transformation. The proposed formalization provides an intuitive description for the manipulation of graph structures as they occur in workflow delegation and a precise specification of consistency conditions on graphs and graph transformations. We specifies a type graph to represents the type information in the graph transformation for workflow delegation, a set of rules to build the system states and sets of positive and negative constraints to specify wanted and unwanted framework.

On structured graph grammars. I

We present an approach for programming with graph transformation rules in which programs can be as efficient as programs in imperative languages. The ba- sic idea is to equip rules and host graphs with distinguished nodes, so-called roots, and to match roots in rules with roots in host graphs. This enables graph transforma- tion rules to be matched in constant time, provided that host graphs have a bounded node degree (which in practice is often the case). Hence, for example, programs with a linear bound on the number of rule applications run in truly linear time. We demonstrate the feasibility of this approach with a case study in graph colouring.

UML state machines are quite popular and useful to specify dynamic components of software systems. They have a formal static semantics but their execution semantics is described only informally. Graph transformation, on the other hand, constitutes a well-studied area with many theoretical results and practical application domains. In this paper, an operational semantics for a subset of UML state machines is proposed which is based on graph transformation. In more detail, a UML state machine is described as a structured graph transformation system in such a way that the wellformedness rules of UML state machines are satisfied and the firing of a (maximum) set of enabled non-conflicting transitions corresponds to the application of a graph transformation rule. The presented approach uses the concept of transformation units, a recently developed modularization concept for graph transformation systems.

Graph rewriting is a powerful technique that requires graph pattern matching, which is an NP-complete problem. We present GrGen, a generative programming system for graph rewriting, which applies heuristic optimizations. According to Varro's benchmark it is at least one order of magnitude faster than any other tool known to us. Our graph rewriting tool implements the well-founded single-pushout approach. We define the notion of search plans to represent different matching strategies and equip these search plans with a cost model, taking the present host graph into account. The task of selecting a good search plan is then viewed as an optimization problem. For the ease of use, GrGen features an expressive specification language and generates program code with a convenient interface.

In this thesis we explore extremal graph theory, focusing on new methods which apply to different notions of regular graph. The first notion is dregularity, which means each vertex of a graph is contained in exactly d edges, and the second notion is Szemeredi regularity, which is a strong, approximate version of this property that relates to pseudorandomness. We begin with a novel method for optimising observables of Gibbs distributions in sparse graphs. The simplest application of the method is to the hard-core model, concerning independent sets in d-regular graphs, where we prove a tight upper bound on an observable known as the occupancy fraction. We also cover applications to matchings and colourings, in each case proving a tight bound on an observable of a Gibbs distribution and deriving an extremal result on the number of a relevant combinatorial structure in regular graphs. The results relate to a wide range of topics including statistical physics and Ramsey theory. We then turn to a form of Szemeredi regularity in sparse hypergraphs, and develop a method for embedding complexes that generalises a widely-applied method for counting in pseudorandom graphs. We prove an inheritance lemma which shows that the neighbourhood of a sparse, regular subgraph of a highly pseudorandom hypergraph typically inherits regularity in a natural way. This shows that we may embed complexes into suitable regular hypergraphs vertex-by-vertex, in much the same way as one can prove a counting lemma for regular graphs. Finally, we consider the multicolour Ramsey number of paths and even cycles. A well-known density argument shows that when the edges of a complete graph on kn vertices are coloured with k colours, one can find a monochromatic path on n vertices. We give an improvement to this bound by exploiting the structure of the densest colour, and use the regularity method to extend the result to even cycles.

Algebraic graph rewriting with controlled embedding