GRAPH GRAMMARS WITH NEGATIVE APPLICATION CONDITIONS

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.

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.

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.

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

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.

Graph Operations, Graph Transformations and Monadic Second-Order Logic A survey

Graph Operations, Graph Transformations and Monadic Second-Order Logic:: A survey

The current marketplace can be characterized by the need for variety, faster time to market, and decrease in cost. To survive companies are shifting from a mass production mode to mass customization to provide the necessary variety. One of the key elements of mass customization is the product platform. In this paper we will investigate the use of graph grammars to develop common platforms for a set of similar products and to specify the product portfolio supported by the platform. To facilitate development of common platforms a formal product family architecture representation is presented which separates the core and the options to facilitate the identification of the common platform. Graphs are used to represent the core for function and structure viewpoints, and grammars to specify the relationships among the core and the options. Arguments on suitability of graph grammars in common platform development, are also presented in the paper.

Given a sample from an unknown probability distribution over strings, there exist algorithms for inferring the structure and parameters of stochastic grammatical representations of the unknown distribution, i.e. string grammars. Despite the fact that research on grammatical representations of sets of graphs has been conducted since the late 1960’s, almost no work has considered the possibility of stochastic graph grammars and no algorithms exist for inferring stochastic graph grammars from data. This paper presents PEGG, an algorithm for estimating the parameters of stochastic context-free graph grammars given a sample from an unknown probability distribution over graphs. It is established formally that for a certain class of graph grammars PEGG finds parameter estimates in polynomial time that maximize the likelihood of the data, and preliminary empirical results demonstrate that the algorithm performs well in practice.KeywordsGraph TransformationGraph GrammarMaximum Likelihood ParameterStart SymbolEstimate Maximum Likelihood ParameterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Vigna and Ghezzi showed that the language of grid graphs could not be constructed by their context-free graph grammars [1]. In this paper, we construct a context-sensitive graph grammar for the two-dimensional grid graphs.

The aim of this paper is to prove that the system of simple graph grammars (Einfache Graph-Grammatiken) in[1]is complete. A graph grammar is a generalization of a Chomsky-grammar which defines a graph language, i.e。a language composed of a set of directed graphs with labelled nodes and arcs。 A system of graph grammars is said to be complete if it satisfies the following property: For each finite set T of labels, the class of all graph languages over T defined by graph grammars of the system is identical with the class of ail recussively enumerable sets of labelled graphs over T. Where a set of labelled graphs over T is recursively enumerable if the associated set of integers by a Godel numbering from the labelled graphs over T into the integers is recursively enumerable。 Several authors have introduced their system of graph grammars (e・g.[11,[21, [31,[41,[51,[6j,[7])。However they did not refer to the completeness of their systems。 The system of simple graph grammars was introduced in[1]as a subsystem of the system in [2]。In this paper we modify the definition of the system in the following manner: A production of our system is an ordered triple(K,F,K’)which consists of two labelled graphs 瓦A7 and a one・to・one function F from a set of nodes of 瓦to a set of nodes of K'. If iK, F, m is a production, and if K occurs in a labelled graph G, then the production is applicable to G, and the effect of the application is to replace an occurrence of K in G by 瓦へ The function F specifies the embedding of 瓦7into the remainder of removing K from G; if a node n' of K' is the image of a node n of K, thenがis put upon the trace of n in the remainder. This is illustrated by Figure O。 The formal definitions of labelled graphs and several concepts with labelled graphs are given in the first section of this paper. The definition of simple graph grammars is given in the second section. In the third section it is proved that the system of simple graph grammars is complete. The final section gives a generalization of the system of simple graph grammars.

A new mechanism for generating graph languages is introduced which is based on the controlled rewriting of graphs using only six elementary types of graph productions, namely the addition, the deletion and the renaming of a node or an edge. Although these elementary graph productions are acting strictly locally and no embedding transformations are needed, in the unrestricted and monotone case, elementary programmed graph grammars have the same generative power as expression graph grammars. As a graph with attributes assigned to its nodes and edges is an even more useful tool for the description of certain data structures than a directed graph, attributed elementary programmed graph grammars turn out to be adequate graph rewriting systems applicable in many areas of computer science.KeywordsEquivalence ClassDirected GraphGraph ProductionGraph GrammarEmpty GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.