Formal foundation of consistent EMF model transformations by algebraic graph transformation

Model transformation is one of the key activities in model-driven software development. An increasingly popular technology to define modeling languages is provided by the Eclipse Modeling Framework (EMF). Several EMF model transformation approaches have been developed, focusing on different transformation aspects. To validate model transformations with respect to functional behavior and correctness, a formal foundation is needed. In this paper, we define consistent EMF model transformations as a restricted class of typed graph transformations using node type inheritance. Containment constraints of EMF model transformations are translated to a special kind of graph transformation rules such that their application leads to consistent transformation results only. Thus, consistent EMF model transformations behave like algebraic graph transformations and the rich theory of algebraic graph transformation can be applied to these EMF model transformations to show functional behavior and correctness. Furthermore, we propose parallel graph transformation as a suitable framework for modeling EMF model transformations with multi-object structures. Rules extended by multi-object structures can specify a flexible number of recurring structures. The actual number of recurring structures is dependent on the application context of such a rule. We illustrate our approach by selected refactorings of simplified statechart models. Finally, we discuss the implementation of our concepts in a tool environment for EMF model transformations.     

Consistent integration of models based on views of meta models

The complexity of large system models in software engineering nowadays is mastered by using different views. View-based modelling aims at creating small, partial models, each one of them describing some aspect of the system. Existing formal techniques supporting view-based visual modelling are based on typed attributed graphs, where views are related by typed attributed graph morphisms. Such morphisms up to now require a meta model given by a fixed type graph, as well as a fixed data signature and domain. This is in general not adequate for view-oriented modeling where only parts of the complete meta model are known and necessary when modelling a partial view of the system. The aim of this paper is to extend the framework of typed attributed graph morphisms to generalized typed attributed graph morphisms, short GAG-morphisms, which involve changes of the type graph, data signature, and domain. This allows the modeller to formulate type hierarchies and views of visual languages defined by GAG-morphisms between type graphs, short GATG-morphisms. In this paper, we study the interaction and integration of views, and the restriction of views along type hierarchies. In the main result, we present suitable conditions for the integration and decomposition of consistent view models (Theorem 4.1) and extend these conditions to view models defined over meta models with constraints (Theorem 5.1). As a running example, we use a visual domain-specific modelling language to model coarse-grained IT components and their connectors in decentralized IT infrastructures. Using constraints, we formulate connection properties as invariants.     

Grammar-based model transformations: Definition,execution, and quality properties

Model transformation is a key concept in model-driven software engineering. The definition of model transformations is usually based on meta-models describing the abstract syntax of languages. While meta-models are thereby able to abstract from superfluous details of concrete syntax, they often loose structural information inherent in languages, like information on model elements always occurring together in particular shapes. As a consequence, model transformations cannot naturally re-use language structures, thus leading to unnecessary complexity in their development as well as in quality assurance.In this paper, we propose a new approach to model transformation development which allows to simplify the developed transformations and improve their quality via the exploitation of the languages׳ structures. The approach is based on context-free graph grammars and transformations defined by pairing productions of source and target grammars. We show that such transformations have important properties: they terminate and are sound, complete, and deterministic.     

A Conceptual and Formal Framework for the Integration of Data Type and Process Modeling Techniques

A conceptual framework for the integration of data type and process modeling techniques, called integration paradigm, has been presented by the authors in previous papers already. The aim of this paper is to give a short review of this conceptual framework and to present a formal model for the integration paradigm. The formal model for the four layers, called data type, data states and transformations, processes and system architecture layers respectively, is based on an integration of abstract data types and structured transition systems. This formal model can be instantiated by all kinds of basic and integrated modeling techniques. Algebraic high-level nets, attributed graph transformation, an integration of Z with statecharts, and some diagram techniques of UML are discussed on the conceptual level. As instantiation of the formal model, a well-known CCS sender specification, place/transition nets, algebraic high-level nets and attributed graph transformation are presented in this paper, while instantiations of other modeling techniques will be discussed elsewhere.     

Behavioral Refinement of Graph Transformation-Based Models

Model-driven software engineering requires the refinement of abstract models into more concrete, platform-specific ones. To create and verify such refinements, behavioral models capturing recon- figuration or communication scenarios are presented as instances of a dynamic meta-model, i.e., a typed graph transformation system specifying the concepts and basic operations scenarios may be composed of. Possible refinement relations between models can now be described based on the corresponding meta-models.In contrast to previous approaches, refinement relations on graph transformation systems are not defined as fixed syntactic mappings between abstract transformation rules and, e.g., concrete rule expressions, but allow for a more loose, semantically defined relation between the transformation systems, resulting in a more flexible notion of refinement.     

Toward a grid-based DBMS

The relational database management system (DBMS) community has been progressing toward using specialized grids. EMC/Acxiom's data grid architecture and MySQL Cluster's grid architecture couple the main memories of PCs with redundancy to implement persistence. In a data grid architecture at its base level is a grid abstract machine, which consists of a collection of typed nodes. The grid abstract machine provides redundant storage in case a node fails. It might also provide interfaces that group nodes into enclaves. This grouping could be based on attributes such as assignment, node type, size, capabilities, physical location, and who owns it. This departs from traditional database implementations, which were tuned to small numbers of processors and in which most algorithms for relational operators and most indices were tuned to disk-block transfers.     

Event-driven grammars: relating abstract and concrete levels of visual languages

In this work we introduce event-driven grammars, a kind of graph grammars that are especially suited for visual modelling environments generated by meta-modelling. Rules in these grammars may be triggered by user actions (such as creating, editing or connecting elements) and in their turn may trigger other user-interface events. Their combination with triple graph transformation systems allows constructing and checking the consistency of the abstract syntax graph while the user is building the concrete syntax model, as well as managing the layout of the concrete syntax representation. As an example of these concepts, we show the definition of a modelling environment for UML sequence diagrams. A discussion is also presented of methodological aspects for the generation of environments for visual languages with multiple views, its connection with triple graph grammars, the formalization of the latter in the double pushout approach and its extension with an inheritance concept. This is a revised and extended version of a paper presented at the ICGT’04 conference, see [21].     

Circle formation of weak robots and Lyndon words

In this paper a discrete-time dynamic random graph process is studied that interleaves the birth of nodes and edges with the death of nodes. In this model, at each time step either a new node is added or an existing node is deleted. A node is added with probability p together with an edge incident on it. The node at the other end of this new edge is chosen based on a linear preferential attachment rule. A node (and all the edges incident on it) is deleted with probability q=1−p. The node to be deleted is chosen based on a probability distribution that favors small-degree nodes, in view of recent empirical findings. We analyze the degree distribution of this model and find that the expected fraction of nodes with degree k in the graph generated by this process decreases asymptotically as k−1−(2p/2p−1).     

Resource-aware policies

In previous papers, we proposed an extension of Spider Diagrams to object-oriented modelling, called Modelling Spider Diagrams (MSDs), as a visual notation for specifying admissible states of instances of types, and for verifying the conformance of configurations of instances with such specifications. Based on this formalisation, we developed a notion of transformation of MSDs, modelling admissible evolutions of configurations. In the original version of MSD, individual instances evolve independently, but in reality evolutions often occur in the context of available resources, so transformations must be extended to take this into account. In this paper we provide an abstract syntax for MSDs, in terms of typed attributed graphs, and a semantics for the specification of policies based on notions from the theory of graph transformations, and we associate with them a notion of resources. We also introduce a synchronisation mechanism, based on annotation of instances with resources, so that the transformations required by a policy occur with respect to available resources. In particular, resources can be atomically produced or consumed or can change their state consistently with the evolution of the spiders subject to the policy.     

无向双环网络的容错路由研究

在节点出现故障的情况下,如何保证网络节点之间的路由是一个重要的问题。将无向双环网络的节点按照最短路径访问方式映射到直角坐标系形成最优路由构图[CG(N;±r,±s)];基于该构图根据源节点和目的节点是否位于坐标轴上以及它们周围的故障节点数,提出故障节点封闭区和逃逸区的概念;存在故障逃逸区的情况下,源、目的节点之间仍然可以进行最优路由,针对出现故障节点封闭区而无法进行最优路由的情况下,增加等价节点形成扩展路由构图[ECG(N;±r,±s)],从而寻找容错路由;给出最优路由构图、扩展路由构图和容错路由的算法,并编程仿真了这些算法。     

PathRank: Ranking nodes on a heterogeneous graph for flexible hybrid recommender systems

We present a flexible hybrid recommender system that can emulate collaborative-filtering, Content-based Filtering, context-aware recommendation, and combinations of any of these recommendation semantics. The recommendation problem is modeled as a problem of finding the most relevant nodes for a given set of query nodes on a heterogeneous graph. However, existing node ranking measures cannot fully exploit the semantics behind the different types of nodes and edges in a heterogeneous graph. To overcome the limitation, we present a novel random walk based node ranking measure, PathRank, by extending the Personalized PageRank algorithm. The proposed measure can produce node ranking results with varying semantics by discriminating the different paths on a heterogeneous graph. The experimental results show that our method can produce more diverse and effective recommendation results compared to existing approaches.     

Parallelism and concurrency of graph manipulations

Graph manipulations are formalized as graph derivations within the framework of graph grammar theory. In this paper we generalize recently published ‘Church–Rosser’ and ‘Parallelism’ Theorems for graph derivations. Given a ‘sequential independent’ sequence of graph derivations G?H ?X the Parallelism Theorem states that there is also a sequential independent sequence via the same productions applied in reverse order, and a direct derivation G ? X via the corresponding parallel production.In our ‘Concurrency Theorem’, the main result of this paper, the assumption of sequential independence is dropped. For each sequence of productions together with dependence relations (allowing later rules to depend on the effects of earlier productions), we construct a single ‘concurrent production’. The Concurrency Theorem states that each graph derivation sequence via the given sequence of productions, which respects all the dependence relations, can be performed in a single direct derivation via the ‘concurrent production’. Moreover this assignment becomes a bijective correspondence.This Concurrency Theorem is formulated and proved in the framework of the algebraic theory of graph grammars using new pushout and pullback lemmas for the 3- and 4- dimensional cubes. As corollaries we obtain the Parallelism Theorem and a theorem reducing the strong to the weak Church–Rosser-property of graph derivations. Applications of these results to various fields in computer science especially to data base systems, are sketched in the introduction.     

Graph Transformation in a Nutshell

Even sophisticated techniques start out from simple ideas. Later, in reply to application needs or theoretical problems new concepts are introduced and new formalisations proposed, often to a point where the original simple core is hardly recognizably. In this paper we provide a non-technical introduction to the basic concepts of typed graph transformation systems, completed by a survey of more advanced concepts, and explain some of its history and motivations.     

Intrinsic graph topological correlation for graph convolutional network propagation

Recently, Graph Convolutional Networks (GCNs) and their variants become popular to learn graph-related tasks. These tasks include link prediction, node classification, and node embedding, among many others. In the node classification problem, the input is a graph with some labeled nodes and the features associated with these nodes and the objective is to predict the unlabeled nodes. While the GCNs have been successfully applied to this problem, some caveats that are inherited from classical deep learning remain unsolved. One such inherited caveat is that, during classification, GCNs only consider the nodes that are a few neighbors away from the labeled nodes. However, considering only a few steps away nodes could not effectively exploit the underlying graph topological information. To remedy this problem, the state-of-the-art methods leverage the network diffusion approaches, such as personalized PageRank and its variants, to fully account for the graph topology. However, these approaches overlook the fact that the network diffusion methods favour high degree nodes in the graph, resulting in the propagation of the labels to the unlabeled,hub nodes. In order to overcome bias, in this paper, we propose to utilize a dimensionality reduction technique, which is conjugate with personalized PageRank. Testing on four real-world networks that are commonly used in benchmarking GCNs’ performance for the node classification task, we systematically evaluate the performance of the proposed methodology and show that our approach outperforms existing methods for wide ranges of parameter values. Since our method requires only a few training epochs, it releases the heavy training burden of GCNs. The source code of the proposed method is freely available at https://github.com/mustafaCoskunAgu/ScNP/blob/master/TRJMain.m.     

An efficient network flow code for finding all minimum cost s–t cutsets

Cutset algorithms have been well documented in the operations research literature. A directed graph is used to model the network, where each node and arc has an associated cost to cut or remove it from the graph. The problem considered in this paper is to determine all minimum cost sets of nodes and/or arcs to cut so that no directed paths exist from a specified source node s to a specified sink node t. By solving the dual maximum flow problem, it is possible to construct a binary relation associated with an optimal maximum flow such that all minimum cost s–t cutsets are identified through the set of closures for this relation. The key to our implementation is the use of graph theoretic techniques to rapidly enumerate this set of closures. Computational results are presented to suggest the efficiency of our approach.Scope and purposeThis paper describes the technical details of a network flow algorithm used to find all minimum cost s–t cutsets in any network topology. The motivation for this work was to provide additional automated analysis capability to a military network targeting system. Specifically, the problem is to identify a minimum cost set of nodes and/or arcs that when removed from the network, will disconnect a selected pair of origin–destination nodes. Algorithms for solving this problem are well understood, with an active research thrust in both the operations research and computer science academic communities in developing more efficient algorithms for larger networks. The main contribution of this paper is in extending these algorithms to quickly find all minimum cost cutset solutions. The implementation described in this paper outperformed conventional methods by several orders of magnitude on networks having thousands of nodes and arcs, with empirical solution times that grew linearly with the network size. The results translate to a real-time cutset analysis capability to support military targeting applications.     

Towards Attributed Graphs in Groove: Work in Progress

Graphs are a very expressive formalism for system modeling, especially when attributes are allowed. Our research is mainly focused on the use of graphs for system verification.Up to now, there are two main different approaches of modeling (typed) attributed graphs and specifying their transformation. Here we report preliminary results of our investigation on a third approach. In our approach we couple a graph to a data signature that consists of unary operations only. Therefore, we transform arbitrary signatures into a structure comparable to what is called a graph structure signature in the literature, and arbitrary algebras into the corresponding algebra graph.     

Type-Safe Code Transformations in Haskell

The use of typed intermediate languages can significantly increase the reliability of a compiler. By type-checking the code produced at each transformation stage, one can identify bugs in the compiler that would otherwise be much harder to find. We propose to take the use of types in compilation a step further by verifying that the transformation itself is type correct, in the sense that it is impossible that it produces an ill typed term given a well typed term as input.We base our approach on higher-order abstract syntax (HOAS), a representation of programs where variables in the object language are represented by meta-variables. We use a representation that accounts for the object language's type system using generalized algebraic data types (GADTs). In this way, the full binding and type structure of the object language is exposed to the host language's type system. In this setting we encode a type preservation property of a CPS conversion in Haskell's type system, using witnesses of a type correctness proof encoded in a GADT.     

CAMAS: A cluster-aware multiagent system for attributed graph clustering

Attributed graphs describe nodes via attribute vectors and also relationships between different nodes via edges. To partition nodes into clusters with tighter correlations, an effective way is applying clustering techniques on attributed graphs based on various criteria such as node connectivity and/or attribute similarity. Even though clusters typically form around nodes with tight edges and similar attributes, existing methods have only focused on one of these two data modalities. In this paper, we comprehend each node as an autonomous agent and develop an accurate and scalable multiagent system for extracting overlapping clusters in attributed graphs. First, a kernel function with a tunable bandwidth factor δ is introduced to measure the influence of each agent, and those agents with highest local influence can be viewed as the “leader” agents. Then, a novel local expansion strategy is proposed, which can be applied by each leader agent to absorb the most relevant followers in the graph. Finally, we design the cluster-aware multiagent system (CAMAS), in which agents communicate with each other freely under an efficient communication mechanism. Using the proposed multiagent system, we are able to uncover the optimal overlapping cluster configuration, i.e. nodes within one cluster are not only connected closely with each other but also with similar attributes. Our method is highly efficient, and the computational time is shown that nearly linearly dependent on the number of edges when δ ∈ [0.5, 1). Finally, applications of the proposed method on a variety of synthetic benchmark graphs and real-life attributed graphs are demonstrated to verify the systematic performance.     

High-level replacement units and their termination properties

Visual rewriting techniques, in particular graph transformations, are increasingly used to model transformations of systems specified through diagrammatic sentences. Several rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism; yet, for many of them, basic results concerning the formal properties of these models are still missing. In this paper, we give a contribution towards solving the termination problem for rewriting systems with external control mechanisms. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For high-level replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. We explore some types of rules and replacement units for which the criterion can be established. These are used to show the termination of some replacement units needed to express model transformations formalizing refactoring.