Canonical Derivations with Negative Application Conditions

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.

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

In graph transformation, a match just represents an occurrences of a rule's left-hand side in the host graph. This is expressed by a morphism preserving the graph structure. However, there are situations where occurrences are bound by additional constraints. These can either be implicit, such as the gluing conditions of the DPO, or explicit such as negative application conditions. In this paper we study another type of implicit condition based on the reflection of structure. Morphisms reflecting some of the structures of their targets are abstractly characterised as open maps in the sense of Joyal, Nielsen, and Winskel. We show that under certain restrictions on the rules, DPOs preserve open maps. We establish an encoding of open maps into negative application conditions and study concurrency properties of the new approach.

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.

Parallelism and Concurrency in Adhesive High-Level Replacement Systems with Negative Application Conditions

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.

The main idea of graph grammars and graph transformation is the rule-based graph rewriting, where the application of every rule graph rule leads to a graph transformation step. Graph grammars can be used to generate graph languages which is similar to Chomsky grammars in formal language theory. Moreover, graphs can be used to model the states of all kinds of systems, which allows one to use graph transformation to model state changes in these systems. A rule-based transformation system may show two kinds of nondeterminism: (1) for each rule can exist several matches, and (2) several rules can be applicable. This paper concentrates on the second non-determinism, studying a method to detect the rules which are not applicable in graph transformation systems, proposing a backward graph transformation conflict detecting algorithm. At first the computation of conflict and dependency of two rules is available by use of AGG . Secondly the set of dependencies has to be tested by Warshall algorithm and the set of conflicts has to be computed by backward algorithm. At last, the termination of graph transformation systems and validity of rules can be detected as well.

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.

On translating UML models into graph transformation systems

In this work we show that the reachability problem for graph transformation systems is in the complexity class XP when parameterized with respect to the depth of derivations and the cutwidth of the source graph. More precisely, we show that for any set \(\mathcal {R}\) of graph transformation rules, one can determine in time \(f(c,d)\cdot |G|\cdot |H|^{g(c,d)}\) whether a graph G of cutwidth c can be transformed into a graph H in depth at most d by the application of graph transformation rules from \(\mathcal {R}\). In particular, our algorithm runs in polynomial time when c and d are constants. On the other hand, we show that the problem becomes NP-hard if we allow \(c=O(|G|)\) and \(d=5\). In the case in which all transformation rules are monotone we get an algorithm running in time \(f(c,d)\cdot |G|^{O(c)}\cdot |H|\). To prove our main theorems we will establish an interesting connection between graph transformation systems and regular slice languages. More precisely, we show that if \(\mathcal {A}\) is a slice automaton representing a set \({\mathcal {L}}_{{\mathcal {G}}}(\mathcal {A})\) of graphs, then one can construct in time linear in \(|\mathcal {A}|\) a slice automaton \(\mathcal {N}(\mathcal {A})\) representing the set of all graphs that can be obtained from graphs in \({\mathcal {L}}_{{\mathcal {G}}}(\mathcal {A})\) by the application of one layer of transformation rules in \(\mathcal {R}\).

Graph Grammars are a visual formal language for which there are several techniques of system specification and verification. This fact makes them an attractive option for describing complex systems. Fuzzy graph grammars generalize the concept of graph grammars, using fuzzy graphs. A fuzzy graph is composed of vertices and edges that have an associated membership value, which varies within a range of 0 to 1. Due to the lack of technique and analysis tools for fuzzy graph grammars, their use is still quite limited. One way to allow the analysis of fuzzy graphs grammars is using the extension of existing graph grammar approaches, including the concept of membership in the graph components. There is a relational approach of graph grammars that allows the use of theorem provers to perform property analysis of systems described in this language. This approach is the basis of a translation of graph grammars into the Event-B language, which enables the use of theorem provers of the Rodin tool. Therefore, the aim of this work is to extend this graph grammar approach, including fuzzy concepts, to allow the use of the theorem proving technique to analyze fuzzy graph grammars. In order to set this extension was first necessary to define the notion of typed fuzzy graph grammars.

Translating Controlled Graph Grammars to Ordinary Graph Grammars

Scenario-driven analysis of systems specified through graph transformations

Model checking is one of the successful techniques in automated verification of software and hardware systems. However, employing this technique for verification of properties such as the safety and liveness requires that all possible states of a system are generated and then the given property is checked. In large and complex systems, generating all states causes the state space explosion problem. Hence, it is possible to refute such properties by searching the state space to find a state in which the given property is violated. Of course, it is possible that detecting such states in complex systems leads to the exhaustive exploration of the state space. Recent researches confirm that using meta-heuristic and evolutionary approaches to intelligently explore a portion of the state space can be a promising idea. Hence, in this paper, we propose an approach based on ant colony optimization algorithm for refuting the safety and liveness properties and also analyzing reachability ones in systems specified formally through graph transformation system. Refutation of liveness and analyzing reachability properties in systems modeled by graph transformations are the prominent advantages of this approach in comparison with the previous approaches. The proposed approach is implemented in GROOVE which is an open source toolset for designing and model checking graph transformation systems. Experimental results show that our proposed approach is faster and it generates shorter counterexamples in comparison with others.