Graphs are ubiquitous in Computer Science. For this reason, in many areas, it is very important to have the means to express and reason about graph properties. In particular, we want to be able to check automatically if a given graph property is satisfiable. Actually, in most application scenarios it is desirable to be able to explore graphs satisfying the graph property if they exist or even to get a complete and compact overview of the graphs satisfying the graph property. We show that the tableau-based reasoning method for graph properties as introduced by Lambers and Orejas paves the way for a symbolic model generation algorithm for graph properties. Graph properties are formulated in a dedicated logic making use of graphs and graph morphisms, which is equivalent to firstorder logic on graphs as introduced by Courcelle. Our parallelizable algorithm gradually generates a finite set of so-called symbolic models, where each symbolic model describes a set of finite graphs (i.e., finite models) satisfying the graph property. The set of symbolic models jointly describes all finite models for the graph property (complete) and does not describe any finite graph violating the graph property (sound). Moreover, no symbolic model is already covered by another one (compact). Finally, the algorithm is able to generate from each symbolic model a minimal finite model immediately and allows for an exploration of further finite models. The algorithm is implemented in the new tool AutoGraph.

This book constitutes the proceedings of the 20th International Conference on Fundamental Approaches to Software Engineering, FASE 2017, which took place in Uppsala, Sweden in April 2017, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017. The 23 papers presented in this volume were carefully reviewed and selected from 91 submissions. They were organized in topical sections named: learning and inference; test selection; program and system analysis; graph modeling and transformation; model transformations; configuration and synthesis; and software product lines.

Software development tools that work and behave consistently across different programming languages are helpful for developers, because they do not have to familiarize themselves with new tooling whenever they decide to use a new language. Also, being able to combine multiple programming languages in a program increases reusability, as developers do not have to recreate software frameworks and libraries in the language they develop in and can reuse existing software instead. However, developers often have a broad choice with regard to tools, some of which are designed for only one specific programming language. Various Integrated Development Environments have support for multiple languages, but are usually unable to provide a consistent programming experience due to different features of language runtimes. Furthermore, common mechanisms that allow reuse of software written in other languages usually use the operating system or a network connection as the abstract layer. Tools, however, often cannot support such indirections well and are therefore less useful in debugging scenarios for example. In this report, we present a novel approach that aims to improve the programming experience with regard to working with multiple high-level programming languages. As part of this approach, we reuse the tools of a Smalltalk programming environment for other languages and build a multi-language virtual execution environment which is able to provide the same runtime capabilities for all languages. The prototype system Squimera is an implementation of our approach and demonstrates that it is possible to reuse development tools, so that they behave in the same way across all supported programming languages. In addition, it provides convenient means to reuse and even mix software libraries and frameworks written in different languages without breaking the debugging experience.

This book constitutes the refereed proceedings of the 14th International Conference on Graph Transformation, ICGT 2021, which took place virtually during June 24-25, 2021. The 14 full papers and 2 tool papers presented in this book were carefully reviewed and selected from 26 submissions. They deal with the following topics: theoretical advances; application domains; and tool presentations.

Today, software has become an intrinsic part of complex distributed embedded real-time systems. The next generation of embedded real-time systems will interconnect the today unconnected systems via complex software parts and the service-oriented paradigm. Therefore besides timed behavior and probabilistic behaviour also structure dynamics, where the architecture can be subject to changes at run-time, e.g. when dynamic binding of service end-points is employed or complex collaborations are established dynamically, is required. However, a modeling and analysis approach that combines all these necessary aspects does not exist so far. To fill the identified gap, we propose Probabilistic Timed Graph Transformation Systems (PTGTSs) as a high-level description language that supports all the necessary aspects of structure dynamics, timed behavior, and probabilistic behavior. We introduce the formal model of PTGTSs in this paper and present a mapping of models with finite state spaces to probabilistic timed automata (PTA) that allows to use the PRISM model checker to analyze PTGTS models with respect to PTCTL properties.

This book constitutes the refereed proceedings of the 29th International Conference on Applications and Theory of Petri Nets and Other Models of Concurrency, PETRI NETS 2008, held in Xi'an, China, in June 2008. The 19 revised full regular papers and 4 revised tool papers presented together with 5 invited papers were carefully reviewed and selected from 75 submissions. All current issues on research and development in the area of Petri nets and modeling of concurrent systems are addressed.

Recent developments in information and communication technology (ICT) have paved the way for a world of advanced communication, intelligent information processing and ubiquitous access to information and services. The ability to work, communicate, interact, conduct business, and enjoy digital entertainment virtually anywhere is r- idly becoming commonplace due to a multitude of small devices, ranging from mobile phones and PDAs to RFID tags and wearable computers. The increasing number of connected devices and the proliferation of networks provide no indication of a sl- down in this tendency. On the negative side, misuse of this same technology entails serious risks in various aspects, such as privacy violations, advanced electronic crime, cyber terrorism, and even enlargement of the digital divide. In extreme cases it may even threaten basic principles and human rights. The aforementioned issues raise an important question: Is our society ready to adopt the technological advances in ubiq- tous networking, next-generation Internet, and pervasive computing? To what extent will it manage to evolve promptly and efficiently to a next-generation society, ado- ing the forthcoming ICT challenges? The Third International ICST Conference on e-Democracy held in Athens, Greece during September 23–25, 2009 focused on the above issues. Through a compreh- sive list of thematic areas under the title “Next-Generation Society: Technological and Legal issues,” the 2009 conference provided comprehensive reports and stimulated discussions on the technological, ethical, legal, and political challenges ahead of us.

While offering significant expressive power, graph transformation systems often come with rather limited capabilities for automated analysis, particularly if systems with many possible initial graphs and large or infinite state spaces are concerned. One approach that tries to overcome these limitations is inductive invariant checking. However, the verification of inductive invariants often requires extensive knowledge about the system in question and faces the approach-inherent challenges of locality and lack of context. To address that, this report discusses k-inductive invariant checking for graph transformation systems as a generalization of inductive invariants. The additional context acquired by taking multiple (k) steps into account is the key difference to inductive invariant checking and is often enough to establish the desired invariants without requiring the iterative development of additional properties. To analyze possibly infinite systems in a finite fashion, we introduce a symbolic encoding for transformation traces using a restricted form of nested application conditions. As its central contribution, this report then presents a formal approach and algorithm to verify graph constraints as k-inductive invariants. We prove the approach's correctness and demonstrate its applicability by means of several examples evaluated with a prototypical implementation of our algorithm.

Symbolic analysis is an intriguing topic in VLSI designs. The analysis methods are crucial for the applications to the parasitic reduction and analog circuit evaluation. However, analyzing circuits symbolically remains a challenging research issue. Therefore, in this book, we survey the recent results as the progress of on-going works rather than as the solution of the field. For parasitic reduction, we approximate a huge amount of electrical parameters into a simplified RLC network. This reduction allows us to handle very large integrated circuits with given memory capacity and CPU time. A symbolic analysis approach reduces the circuit according to the network topology. Thus, the designer can maintain the meaning of the original network and perform the analysis hierarchically. For analog circuit designs, symbolic analysis provides the relation between the tunable parameters and the characteristics of the circuit. The analysis allows us to optimize the circuit behavior. The book is divided into three parts. Part I touches on the basics of circuit analysis in time domain and in s domain. For an s domain expression, the Taylor's expansion with s approaching infinity is equivalent to the time domain solution after the inverse Laplace transform. On the other hand, the Taylor's expansion when s approaches zero derives the moments of the output responses in time domain. Part II focuses on the techniques for parasitic reduction. In Chapter 2, we present the approximation methods to match the first few moments with reduced circuit orders. In Chapter 3, we apply the Y-Delta transformation to reduce the dynamic linear network. The method finds the exact values of the low order coefficients of the numerator and denominator of the transfer function and thus matches part of the moments. In Chapter 4, we handle two major issues of the Y-Delta transformation: common factors in fractional expressions and round-off errors. Chapter 5 explains the stability of the reduced expression, in particular the Ruth-Hurwitz Criterion. We make an effort to describe the proof of the Criterion because the details are omitted in most of the contemporary textbooks. In Chapter 6, we present techniques to synthesize circuits to approximate the reduced expressions after the transformation. In Part III, we discuss symbolic generation of the determinants and cofactors for the application to analog designs. In Chapter 7, we depict the classical topological analysis approach. In Chapter 8, we describe a determinant decision diagram approach that exploits the sparsity of the matrix to accelerate the computation. In Chapter 9, we take only significant terms when we search through determinant decision diagram to approximate the solution. In Chapter 10, we extend the determinant decision diagram to a hierarchical model. The construction of the modules through the hierarchy is similar to the Y-Delta transformation in the sense that a byproduct of common factors appears in the numerator and denominator. Therefore, we describe the method to prune the common factors.

What does the Web look like? How can we find patterns, communities, outliers, in a social network? Which are the most central nodes in a network? These are the questions that motivate this work. Networks and graphs appear in many diverse settings, for example in social networks, computer-communication networks (intrusion detection, traffic management), protein-protein interaction networks in biology, document-text bipartite graphs in text retrieval, person-account graphs in financial fraud detection, and others. In this work, first we list several surprising patterns that real graphs tend to follow. Then we give a detailed list of generators that try to mirror these patterns. Generators are important, because they can help with "what if" scenarios, extrapolations, and anonymization. Then we provide a list of powerful tools for graph analysis, and specifically spectral methods (Singular Value Decomposition (SVD)), tensors, and case studies like the famous "pageRank" algorithm and the "HITS" algorithm for ranking web search results. Finally, we conclude with a survey of tools and observations from related fields like sociology, which provide complementary viewpoints. Table of Contents: Introduction / Patterns in Static Graphs / Patterns in Evolving Graphs / Patterns in Weighted Graphs / Discussion: The Structure of Specific Graphs / Discussion: Power Laws and Deviations / Summary of Patterns / Graph Generators / Preferential Attachment and Variants / Incorporating Geographical Information / The RMat / Graph Generation by Kronecker Multiplication / Summary and Practitioner's Guide / SVD, Random Walks, and Tensors / Tensors / Community Detection / Influence/Virus Propagation and Immunization / Case Studies / Social Networks / Other Related Work / Conclusions