Grzegorz Rozenberg

Ugo Montanari

Hartmut Ehrig

Hans-jorg Kreowski

Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact, within the area of graph grammars, graph transformation is considered as a fundamental computation paradigm where computation includes specification, programming, and implementation. Over the last three decades, graph grammars have developed at a steady pace into a theoretically attractive and important-for-applications research field.Volume 3 of the indispensable Handbook of Graph Grammars and Computing by Graph Transformations presents the research on concurrency, parallelism, and distribution — important paradigms of modern computer science. The topics considered include semantics for concurrent systems, modeling of concurrency, mobile and coordinated systems, algebraic specifications, Petri nets, visual design of distributed systems, and distributed algorithms. The contributions have been written in a tutorial/survey style by the top experts.

Handbook Of Graph Grammars And Computing By Graph Transformations, Vol 3: Concurrency, Parallelism, And Distribution

Ingo Claben

A Romano

Dietmar Wolz

The complex processes of state changes can be interpreted by resorting to Statistical Quantum Mechanics. However, it is well known that a phenomenological description of state changes can be obtained by using the classical continuum theory. This book supplies a panoramic picture of known and new mathematical models which are suitable to describe phase changes from a macroscopic view point. All these models are derived from the theory of continuous systems with a nonmaterial interface and allow to describe processes of solidification, melting, and vaporization. The nonlocal continuum theory of systems with a non material interface provides a more complex mathematical model in dealing with crystal growth either in a pure melt or in a mixture. A chapter is devoted to the analysis of phase changes in ferroelectric and ferromagnetic crystals.

Thermomechanics Of Phase Transitions In Classical Field Theory

Andrea Corradini

Leila Ribeiro

This book constitutes the refereed proceedings of the Third International Conference on Graph Transformations, ICGT 2006. The book presents 28 revised full papers together with 3 invited lectures. All current aspects in graph drawing are addressed including graph theory and graph algorithms, theoretic and semantic aspects, modeling, tool issues and more. Also includes accounts of a tutorial on foundations and applications of graph transformations, and of ICGT Conference satellite events.

Third International Conference, ICGT 2006, Rio Grande do Norte, Brazil, September 17-23, 2006, Proceedings

Graph Transformations

Abstract: "The algebraic approaches to graph transformation are based on the concept of gluing of graphs corresponding to pushouts in suitable categories of graphs and graph morphisms. This allows one to give not only an explicit algebraic or set theoretical description of the constructions but also to use concepts and results from category theory in order to build up a rich theory and to give elegant proofs even in complex situations. In the previous chapter we have presented an overview of the basic notions and problems common to the two algebraic approaches, the double-pushout (DPO) approach and the single-pushout (SPO) approach, and their solutions in the DPO-approach. In this chapter we introduce the SPO- approach to graph transformation and some of its main results. We study application conditions for graph productions and the transformation of more general structures than graphs in the SPO-approach, where similar generalizations have been or could be studied also in the DPO-approach. Finally, we present a detailed comparison of the DPO and the SPO-approach, especially concerning the solutions to the problems discussed for both approaches in the previous chapter."

Part II: Single Pushout Approach and Comparison with Double Pushout Approach

Algebraic Approaches to Graph Transformation

Third International Conference, ICGT 2006, Rio Grande Do Norte, Brazil, September 17-23, 2006, Proceedings

Engelbert Westkämper

Jörg Desel

Werner Damm

Wolfgang Reif

Eckehard Schnieder

Martin Große-Rhode

This book constitutes the documentation of the scientific outcome of the priority program Integration of Software Specification Techniques for Applications in Engineering sponsored by the German Research Foundation (DFG). It includes main contributions of the projects of the priority program and of additional international experts in the field. Some of the papers included were presented at the related Third International Workshop on the topic, INT 2004, held in Barcelona, Spain in March 2004. The 25 revised full papers presented together with 6 section introductions by the volume editors were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on reference case study production automation, reference case study traffic control systems, petri nets and related approaches in engineering, charts, verification, and integration modeling.

Priority Program SoftSpez of the German Research Foundation (DFG) Final Report

Integration of Software Specification Techniques for Applications in Engineering

Bernd Mahr

Since the early seventies concepts of specification have become central in the whole area of computer science. Especially algebraic specification techniques for abstract data types and software systems have gained considerable importance in recent years. They have not only played a central role in the theory of data type specification, but meanwhile have had a remarkable influence on programming language design, system architectures, arid software tools and environments. The fundamentals of algebraic specification lay a basis for teaching, research, and development in all those fields of computer science where algebraic techniques are the subject or are used with advantage on a conceptual level. Such a basis, however, we do not regard to be a synopsis of all the different approaches and achievements but rather a consistently developed theory. Such a theory should mainly emphasize elaboration of basic concepts from one point of view and, in a rigorous way, reach the state of the art in the field. We understand fundamentals in this context as: 1. Fundamentals in the sense of a carefully motivated introduction to algebraic specification, which is understandable for computer scientists and mathematicians. 2. Fundamentals in the sense of mathematical theories which are the basis for precise definitions, constructions, results, and correctness proofs. 3. Fundamentals in the sense of concepts from computer science, which are introduced on a conceptual level and formalized in mathematical terms.

Module Specifications and Constraints

Fundamentals of Algebraic Specification 2

Priority Program SoftSpez of the German Research Foundation (DFG). Final Report

Hans-Jörg Kreowski

Horst Herrlich

Gerhard Preuß

This volume contains selected papers of the International Workshop on "Categorical Methods in Computer Science - with Aspects from Topology" and of the "6th International Data Type Workshop" held in August/September 1988 in Berlin. The 23 papers of this volume are grouped into three parts: Part 1 includes papers on categorical foundations and fundamental concepts from category theory in computer science. Part 2 presents applications of categorical methods to algebraic specification languages and techniques, data types, data bases, programming, and process specifications. Part 3 comprises papers on categorial aspects from topology which mainly concentrate on special adjoint situations like cartesian closeness, Galois connections, reflections, and coreflections which are of growing interest in categorical topology and computer science.

With Aspects from Topology

Categorical Methods in Computer Science

ICGT 2002 was the ?rst International Conference on Graph Transformation following a series of six international workshops on graph grammars with - plications in computer science, held in Bad Honnef (1978), Osnabruc ̈ k (1982), Warrenton (1986), Bremen (1990), Williamsburg (1994), and Paderborn (1998). ICGT 2002 was held in Barcelona (Spain), October 7–12, 2002 under the a- pices of the European Association of Theoretical Computer Science (EATCS), the European Association of Software Science and Technology (EASST), and the IFIP Working Group 1.3, Foundations of Systems Speci?cation. The scope of the conference concerned graphical structures of various kinds (like graphs, diagrams, visual sentences and others) that are useful to describe complex structures and systems in a direct and intuitive way. These structures are often augmented by formalisms which add to the static description a further dimension, allowing for the modeling of the evolution of systems via all kinds of transformations of such graphical structures. The ?eld of Graph Transformation is concerned with the theory, applications, and implementation issues of such formalisms. The theory is strongly related to areas such as graph theory and graph - gorithms, formal language and parsing theory, the theory of concurrent and distributed systems, formal speci?cation and veri?cation, logic, and semantics.

First International Conference, ICGT 2002, Barcelona, Spain, October 7-12, 2002, Proceedings

Graph Transformation

Wolfgang Reisig

Herbert Weber

This state-of-the-art survey in the Advances in Petri Nets series reports how various well-established and novel Petri net notions and techniques can be employed for modelling communication-based systems, with a particular focus on workflow management and business processes. The book builds on the success of a special program of the German Science Foundation (DFG) on Petri Net Technology as well as on broad participation from the international Petri net research community.

Advances in Petri Nets

Petri Net Technology for Communication-Based Systems

Andy Schürr

Arend Rensink

Graphs are among the simplest and most universal models for a variety of s- tems, not just in computer science, but throughout engineering and the life sciences. When systems evolve we are interested in the way they change, to p- dict, support, or react to their evolution. Graph transformation combines the idea of graphs as a universal modelling paradigm with a rule-based approach to specify their evolution. The area is concerned with both the theory of graph transformation and their application to a variety of domains. The biannual International Conferences on Graph Transformation aim at bringingtogetherresearchersandpractitionersinterestedin the foundations and applicationsof graphtransformation.The ?fth conference,ICGT 2010,was held at the University of Twente (The Netherlands) in September/October 2010, alongwith severalsatellite events.It continuedthe line ofconferences previously held in Barcelona (Spain) in 2002, Rome (Italy) 2004, Natal (Brazil) in 2006 and Leicester (UK) in 2008, as well as a series of six International Workshops on Graph Transformation with Applications in Computer Science from 1978 to 1998. Also, ICGT alternates with the workshop series on Application of Graph Transformation with Industrial Relevance (AGTIVE). The conference was held under the auspices of EATCS and EASST.

5th International Conference, ICGT 2010, Twente, The Netherlands, September 27--October 2, 2010, Proceedings

Gabriel Juhas

Julia Padberg

Since their introduction nearly 40 years ago, research on Petri nets has diverged in many different directions. Various classes of Petri net, motivated either by theory or applications, with its own specific features and methods of analysis, have been proposed and studies in depth. These successful developments have led to a very heterogeneous landscape of diverse models, and this, in turn, has stimulated research on concepts and approaches that contribute to unifying and structuring the diverse landscape. This state-of-the-art survey presents the most relevant approaches to unifying Petri nets in a systematic and coherent way. The 14 chapters written by leading researchers are organized in topical sections on application-oriented approaches, unifying frameworks, and theoretical approaches.

Unifying Petri Nets

Claudia Ermel

Ulrike Golas

Frank Hermann

This book is a comprehensive explanation of graph and model transformation. It contains a detailed introduction, including basic results and applications of the algebraic theory of graph transformations, and references to the historical context. Then in the main part the book contains detailed chapters on M-adhesive categories, M-adhesive transformation systems, and multi-amalgamated transformations, and model transformation based on triple graph grammars. In the final part of the book the authors examine application of the techniques in various domains, including chapters on case studies and tool support. The book will be of interest to researchers and practitioners in the areas of theoretical computer science, software engineering, concurrent and distributed systems, and visual modelling.

General Framework and Applications

Graph and Model Transformation

This state-of-the-art survey in the Advances in Petri Nets series reports how various well-established and novel Petri net notions and techniques can be employed for modelling communication-based systems, with a particular focus on workflow management and business processes.The book builds on the success of a special program of the German Science Foundation (DFG) on Petri Net Technology as well as on broad participation from the international Petri net research community.

Christiane Floyd

Maurice Nivat

James Thatcher

Volume 1: Colloquium on Trees in Algebra and Programming (CAAP'85)

Mathematical Foundations of Software Development. Proceedings of the International Joint Conference on Theory and Practice of Software Development (TAPSOFT), Berlin, March 25-29, 1985

Alfio Martini

Daltro Nunes

Abstract: "Graph Grammars provide an intuitive description for the manipulation of complex structures based on graphs, for instance, data base systems, operating systems, and complex applicative software in general. The algebraic theory of graph grammars is a tentative to describe graph grammars and the gluing construction for graphs as the basic concepts for the construction of derivations. This report consists of four sections. In the first one we present a series of definitions and elementary results concerning graphs, graph morphisms and congruences on graphs, aiming at both establishing terminology for further sections, as well as making it as self-contained as possible. The second section introduces carefully and with extreme detail the formal description of a graph derivation and its abstract (categorical) properties. The third is based heavily upon the second in order to introduce the notion of graph derivation within the double-pushout approach (short DPA), while the last one presents some nice theoretical results concerning Church-Rosser properties and parallelism of graph derivations."

An Introduction to the Double Pushout Approach

Graph Grammars

Hans-Jrg Kreowski

Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others. The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact, within the area of graph grammars, graph transformation is considered a fundamental computation paradigm where computation includes specification, programming, and implementation. Over the last three decades, graph grammars have developed at a steady pace into a theoretically attractive and important-for-applications research field. Volume 3 of the 'indispensable Handbook of' Graph Grammars and Computing by Graph Transformations presents the research on concurrency, parallelism, and distribution -- important paradigms of modern science. The topics considered include semantics for concurrent systems, modeling of concurrency, mobile and coordinated systems, algebraic specifications, Petri nets, visual design of distributed systems, and distributed algorithms. The contributions have been written in a tutorial/survey style by the top experts.

Handbook of Graph Grammars and Computing by Graph Transformation

Hartmut Ehrig

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