Graph Transformation Systems Research Articles

Finitary -adhesive categories

Finitary$\mathcal{M}$-adhesive categories are$\mathcal{M}$-adhesive categories with finite objects only, where$\mathcal{M}$-adhesive categories are a slight generalisation of weak adhesive high-level replacement (HLR) categories. We say an object is finite if it has a finite number of$\mathcal{M}$-subobjects. In this paper, we show that in finitary$\mathcal{M}$-adhesive categories we not only have all the well-known HLR properties of weak adhesive HLR categories, which are already valid for$\mathcal{M}$-adhesive categories, but also all the additional HLR requirements needed to prove classical results including the Local Church-Rosser, Parallelism, Concurrency, Embedding, Extension and Local Confluence Theorems, where the last of these is based on critical pairs. More precisely, we are able to show that finitary$\mathcal{M}$-adhesive categories have a unique$\mathcal{E}$-$\mathcal{M}$factorisation and initial pushouts, and the existence of an$\mathcal{M}$-initial object implies we also have finite coproducts and a unique$\mathcal{E}$′-$\mathcal{M}$pair factorisation. Moreover, we can show that the finitary restriction of each$\mathcal{M}$-adhesive category is a finitary$\mathcal{M}$-adhesive category, and finitarity is preserved under functor and comma category constructions based on$\mathcal{M}$-adhesive categories. This means that all the classical results are also valid for corresponding finitary$\mathcal{M}$-adhesive transformation systems including several kinds of finitary graph and Petri net transformation systems. Finally, we discuss how some of the results can be extended to non-$\mathcal{M}$-adhesive categories.

Formal analysis of model transformations based on triple graph grammars

Triple graph grammars (TGGs) are a well-established concept for the specification and execution of bidirectional model transformations within model driven software engineering. Their main advantage is an automatic generation of operational rules for forward and backward model transformations, which simplifies specification and enhances usability as well as consistency. In this paper we present several important results for analysing model transformations based on the formal categorical foundation of TGGs within the framework of attributed graph transformation systems.Our first main result shows that the crucial properties of correctness and completeness are ensured for model transformations. In order to analyse functional behaviour, we generate a new kind of operational rule, called aforward translation rule. We apply existing results for the analysis of local confluence for attributed graph transformation systems. As additional main results, we provide sufficient criteria for the verification of functional behaviour as well as a necessary and sufficient condition for strong functional behaviour. In fact, these conditions imply polynomial complexity for the execution of the model transformation. We also analyse information and complete information preservation of model transformations, that is, whether a source model can be reconstructed (uniquely) from the target model computed by the model transformation. We illustrate the results for the well-known model transformation example from class diagrams to relational database models.

A Formal Architectural Style for Designing Multi-agent Systems

Architectural styles include specific features which restrict the activities scope, an inevitable fact in software engineering. The appropriate selection of an architectural style is essential in the implementation phases. The attempt is made here to integrate the architecture concept with artificial intelligence, in specific its multi-agent system. The attempt is made here to realize the Artificial Intelligence system’s concept, the agent oriented systems in specific and assess the style concept and its implementation in multi-agent systems. By assessing the available styles and their drawbacks a new multi-purpose style is introduced for agent orientation. This style consists of four style concepts and analyzes all aspects of agent orientated system. This style is modeled through graph transformation system in order to be conceivable dynamically and be checked by a tool named GROOVE which automatically confirms lack of errors in this proposed style.

Decidability Results for Well-structured Graph Transformation Systems

Decidability Results for Well-structured Graph Transformation Systems

QoS contract preservation through dynamic reconfiguration: A formal semantics approach

The increasing pervasiveness of computing services in everyday life, combined with the dynamic nature of their execution contexts, constitutes a major challenge in guaranteeing the expected quality of such services at runtime. Quality of Service (QoS) contracts have been proposed to specify expected quality levels (QoS levels) on different context conditions, with different enforcing mechanisms. In this paper we present a definition for QoS contracts as a high-level policy for governing the behavior of software systems that self-adapt at runtime in response to context changes. To realize this contract definition, we specify its formal semantics and implement it in a software framework able to execute and reconfigure software applications, in order to maintain fulfilled their associated QoS contracts. The contribution of this paper is threefold. First, we extend typed-attributed graph transformation systems and finite-state machines, and use them as denotations to specify the semantics of QoS contracts. Second, this semantics makes it possible to systematically exploit design patterns at runtime by dynamically deploying them in the managed software application. Third, our semantics guarantees self-adaptive properties such as reliability and robustness in the contract satisfaction. Finally, we evaluate the applicability of our semantics implementation by integrating and executing it in FraSCAti, a multi-scale component-based middleware, in three case studies.

Spider Graphs: a graph transformation system for spider diagrams

The use of diagrammatic logic as a reasoning mechanism to produce inferences on subsets of some universe could provide a way to overcome the current limitations of visual modelling methods, which have to be integrated with textual languages to express complex constraints. On the other hand, graph transformations are becoming widespread as a way to express formal semantics for visual modelling languages, so that a mechanisation of diagrammatic logic based on graph transformation would facilitate language integration, based on a common underlying machinery. In this paper, we propose such a mechanisation for spider diagrams (SDs), an established language for reasoning with diagrams modelling relations between sets and constraints on their cardinalities. The concrete syntax of SDs extends that of Euler diagrams that use closed curves and the enclosed regions to represent sets and their intersections. The language is augmented with reasoning rules, i.e. syntactic transformation rules corresponding to logical inference rules. However, these rules are typically defined in procedural terms, so that a completely formal specification and an adequate mechanisation of them has not been achieved yet. We propose an abstract syntax for SDs in terms of typed graphs and define the corresponding language of Spider Graphs (SGs), expressing reasoning rules for SDs as graph transformation units. This enables a direct realisation of the reasoning system via graph transformation tools without resorting to ad hoc implementations, and we provide an implementation in AGG. Techniques for static analysis become available to reason on proof strategies and on possible optimisations.

Deduction as Reduction, from a Categorical Point of View

Deduction systems and graph transformation systems are compared within a common categorical framework. This comparison results in a proposal for a new deduction method in diagrammatic logics, allowing the deletion of intermediate lemmas.

Designing an Architectural Style for Pervasive Healthcare Systems

Nowadays, the Pervasive Healthcare (PH) systems are considered as an important research area. These systems have a dynamic structure and configuration. Therefore, an appropriate method for designing such systems is necessary. The Publish/Subscribe Architecture (pub/sub) is one of the convenient architectures to support such systems. PH systems are safety critical; hence, errors can bring disastrous results. To prevent such problems, a powerful analytical tool is required. So using a proper formal language like graph transformation systems for developing of these systems seems necessary. But even if software engineers use such high level methodologies, errors may occur in the system under design. Hence, it should be investigated automatically and formally that whether this model of system satisfies all their requirements or not. In this paper, a dynamic architectural style for developing PH systems is presented. Then, the behavior of these systems is modeled and evaluated using GROOVE toolset. The results of the analysis show its high reliability.

Scenario-driven analysis of systems specified through graph transformations

Model checking is one of the most accurate analysis techniques which are used to verify software and hardware systems. However, the analysis of large and complex systems tends to become infeasible since their state spaces easily become too big. Besides well-known abstraction techniques, which may hamper the accuracy of results, in this paper we propose the use of scenario-driven model checking to address and mitigate the state explosion problem. The proposal starts from systems specified through a Graph Transformation (GT) system and it is focused on the analysis of the most significant scenarios. We exploit the modularity of GT systems to reduce the state space by eliminating all the nodes and rules that are not involved in the scenario. Focused analysis also helps concentrate on the most critical behaviors of the system and smooth the risks associated with them. The paper introduces the analysis approach and explains how scenarios (specified in terms of sequence diagrams) can help to reduce the state space. All main concepts are illustrated through a simple application for a travel agency specified as if it were a service-oriented application.

On Modelling Communication in Ubiquitous Computing Systems using Algebraic Higher Order Nets

Ubiquitous computing systems (UCSs) are designed to participate almostimperceptibly in everyday life. To ensure a solid operation, a UCS heavily depends on a reliable and efficient communication between its distributed computing components. Moreover components can join and leave the system at any time.In order to guarantee high quality systems, the use of models is inevitable especiallyat an early stage of the development process where models are the only possibilityto address a system which does not yet exist in reality. Petri nets and graph transformationsystems are established, theoretically well-founded concepts for modellingand analysing complex systems.This paper presents a formal approach for modelling core aspects of the communicationin UCSs by using Algebraic Higher Order Nets with Individual Tokens andgraph transformation. The approach is suitable to cover the different aspects ofcommunication and enables the analysis of specific properties. The approach and itssuitability are illustrated based on a running example. The feasibility of embeddingthe approach in a broader context of modelling is demonstrated in applying it to areal world system: the Living Place Hamburg.

ℳ-Adhesive Transformation Systems with Nested Application Conditions. Part 2: Embedding, Critical Pairs and Local Confluence

Graph transformation systems have been studied extensively and applied to several areas of computer science like formal language theory, the modeling of databases, concurrent or distributed systems, and visual, logical, and functional programming. In most kinds of applications it is necessary to have the possibility of restricting the applicability of rules. This is usually done by means of application conditions. In this paper, we continue the work of extending the fundamental theory of graph transformation to the case where rules may use arbitrary (nested) application conditions. More precisely, we generalize the Embedding theorem, and we study how local confluence can be checked in this context. In particular, we define a new notion of critical pair which allows us to formulate and prove a Local Confluence Theorem for the general case of rules with nested application conditions. All our results are presented, not for a specific class of graphs, but for any arbitrary M-adhesive category, which means that our results apply to most kinds of graphical structures. We demonstrate our theory on the modeling of an elevator control by a typed graph transformation system with positive and negative application conditions.

Lazy Graph Transformation

Applying an attributed graph transformation rule to a given object graph always implies some kind of constraint solving. In many cases, the given constraints are almost trivial to solve. For instance, this is the case when a rule describes a transformation G ⇒ H, where the attributes of H are obtained by some simple computation from the attributes of G. However there are many other cases where the constraints to solve may be not so trivial and, moreover, may have several answers. This is the case, for instance, when the transformation process includes some kind of searching. In the current approaches to attributed graph transformation these constraints must be completely solved when defining the matching of the given transformation rule. This kind of early binding is well-known from other areas of Computer Science to be inadequate. For instance, the solution chosen for the constraints associated to a given transformation step may be not fully adequate, meaning that later, in the search for a better solution, we may need to backtrack this transformation step. In this paper, based on our previous work on the use of symbolic graphs to deal with different aspects related with attributed graphs, including attributed graph transformation, we present a new approach that, based on the new notion of narrowing graph transformation rule, allows us to delay constraint solving when doing attributed graph transformation, in a way that resembles lazy computation. For this reason, we have called lazy this new kind of transformation. Moreover, we show that the approach is sound and complete with respect to standard attributed graph transformation. A running example, where a graph transformation system describes some basic operations of a travel agency, shows the practical interest of the approach.

Modular performance modelling for mobile applications (abstracts only)

We propose a model-based approach to analysing the performance of mobile applications where physical mobility and state changes are modelled by graph transformations from which a model in the Performance Evaluation Process Algebra (PEPA) is derived. To fight scalability problems with state space generation we adopt a modular solution where the graph transformation system is decomposed into views, for which labelled transition systems (LTS) are generated separately and later synchronised in PEPA.We demonstrate that the result of this modular analysis is equivalent to that of the monolithic approach and evaluate practicality and scalability by means of a case study.

Verification and validation of model refinement implemented through graph transformation systems

Today, model refinement has a key role in software engineering. It is very important to find an approach to add details to the abstract models. This stepwise refinement should continue till the final software is developed. Since this process in most of the cases is boring, long and error prone, it is crucial to find an automatic yet precise approach to perform refinement. In this paper, we present an accurate approach to refine abstract models into more detailed models. To do so, we use graph transformation systems. In the proposed approach, at first, we design the initial abstract model by graph transforming systems. Then, based on the desired meta-model, we design proper rules to generate a more detailed model from the abstract one, automatically. In this approach, both structural and behavioral parts are considered for modeling. At the end, using the formal background of graph transformations we prove the soundness of the approach. Key words: Model refinement, graph transformation systems.

Structured Operational Semantics for Graph Rewriting

Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in general. Hence, the goal of this article is to obtain a compositional semantics for graph transformation system in analogy to the structural operational semantics (SOS) for Milner's Calculus of Communicating Systems (CCS). The paper introduces an SOS style axiomatization of the standard labelled transition semantics for graph transformation systems. The first result is its equivalence with the so-called Borrowed Context technique. Unfortunately, the axiomatization is not compositional in the expected manner as no rule captures "internal" communication of sub-systems. The main result states that such a rule is derivable if the given graph transformation system enjoys a certain property, which we call "complementarity of actions". Archetypal examples of such systems are interaction nets. We also discuss problems that arise if "complementarity of actions" is violated.

Style-based modeling and verification of fault tolerance service oriented architectures

Abstract Service-Oriented Architecture (SOA) is a flexible, loosely coupled and dynamic architecture for developing different distributed systems. Since using this architecture is every day increasing in the design of software systems, creating dependable services in this architecture is one of the main challenges. Considering different QoS levels consisting of non-functional aspects like security, safety; accessibility, etc is necessary for dependable systems. One of these non-functional aspects is fault tolerance. In this paper, in order to have a fault tolerance system, initially SOA core style has been extended using required parameters. Then, different communication and reconfiguration mechanisms of fault tolerance have been developed by graph transformation rules. Finally, the proposed model has been verified using model checking techniques available for graph transformation systems.

A decentralised graphical implementation of mobile ambients

We present a graphical implementation for finite processes of the mobile ambients calculus. Our encoding uses unstructured (i.e., non-hierarchical) graphs and it is sound and complete with respect to the structural congruence of the calculus (i.e., two processes are equivalent iff mapped to isomorphic graphs). With respect to alternative proposals for the graphical implementation of mobile ambients, our encoding distinguishes the syntactic structure of a process from the activation order of its components. Our solution faithfully captures a basic feature of the calculus (ambients can be nested and reductions are propagated across the nesting) and it allows to model the reduction semantics via a graph transformation system containing just three rules.

UML-BASED MODELING AND ANALYSIS OF SECURITY THREATS

Poor design has been a major source of software security problems. Rigorous and designer-friendly methodologies for modeling and analyzing secure software are highly desirable. A formal method for software development, however, often suffers from a gap between the rigidity of the method and the informal nature of system requirements. To narrow this gap, this paper presents a UML-based framework for modeling and analyzing security threats (i.e. potential security attacks) rigorously and visually. We model the intended functions of a software application with UML statechart diagrams and the security threats with sequence diagrams, respectively. Statechart diagrams are automatically converted into a graph transformation system, which has a well-established theoretical foundation. Method invocations in a sequence diagram of a security threat are interpreted as a sequence of paired graph transformations. Therefore, the analysis of a security threat is conducted through simulating the state transitions from an initial state to a final state triggered by method invocations. In our approach, designers directly work with UML diagrams to visually model system behaviors and security threats while threats can still be rigorously analyzed based on graph transformation.

FORMAL ANALYSIS OF UML 2.0 ACTIVITIES USING GRAPH TRANSFORMATION SYSTEMS

Graph transformation is a general visual modeling language which is suitable for stating the dynamic semantics of the designed models formally. We present a highly understandable yet precise approach to formally define the behavioral semantics of UML 2.0 Activity diagrams by using graph transformation. In our approach we take into account control flow and data flow semantics. Our proposed semantics is based on token-like semantics and traverse-to-completion. The main advantage of our approach is automated formal verification and analysis of UML Activities. We use AGG to design Activities and we use our previous approach to model checking graph transformation system. Hereby, designers can verify and analyze designed Activity diagrams. Since workflow modeling is one of the main application areas of the Activities, we use our proposed semantics for modeling and verification of workflows to illustrate our approach.

Efficient Analysis of Permutation Equivalence of Graph Derivations Based on Petri Nets

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.