Hartmut Ehrig Bücher

The book covers a comprehensive exploration of automata through various frameworks and theories. It begins with a unified representation of different types of automata, including deterministic, nondeterministic, stochastic, and topological, alongside their relation to monoidal categories. Key problems in automata theory are addressed, focusing on behavior, reduction, minimization, and realization of deterministic and nondeterministic automata, as well as transition monoids and structure theory. The text delves into general concepts of reduction and minimization, presenting systematic approaches and relevant theorems. It further examines the behavior of automata in closed categories, emphasizing deterministic cases, and discusses the implications of machine morphisms and behavior characterization. In pseudoclosed categories, the book explores nondeterministic automata, detailing their behavior and reduction processes. It also introduces power automata and initial automata, highlighting their construction, realization, and minimization techniques. The concept of scoop minimization is presented, along with a thorough structure theory of automata, which includes constructions of various automata types and characterizations of morphisms. An appendix provides foundational notions of category theory, encompassing essential concepts such as categories, diagrams, functors, and transformations. The book is a vital resource for und

Frontmatter -- Vorwort -- Inhaltsverzeichnis -- Einleitung -- 1. Kategorien -- 2. Automaten -- 3. Limites in Kategorien -- 4. Universelle Konstruktionen von Automaten -- 5. Funktoren, Limites und adjungierte Funktoren -- 6. Schaltoperationen und Zerlegungen -- Bezeichnungen -- Literatur -- Sachregister -- Backmatter

In fünf sorgfältig aufeinander abgestimmten Teilen behandelt das Buch die wesentlichen mathematischen Elemente der formalen Spezifikation von Systemen und der Aussagen- und Prädikatenlogik, die für das Verständnis des formalisierten Problemlösens entscheidend und damit für Informatiker unerläßlich sind. Eine Einführung in die intuitive Mengentheorie vermittelt zunächst notwendige mathematische Grundlagen. Motiviert durch das Konzept von Datenstrukturen und abstrakten Datentypen werden dann algebraische Strukturen in der Informatik behandelt. Danach werden Aussagen- und Prädikatenlogik aus der Sicht der Mathematik und Informatik dargestellt. Schließlich führt die Kategorientheorie für Informatiker in die Welt der abstrakten Behandlung mathematischer Strukturen ein.Die Neuauflage wurde erweitert um Darstellungen zur Modellalgebra und zur Implementierung. Übungsaufgaben wurden ergänzt.

Focusing on the core principles of algebra, this book provides a comprehensive introduction to the subject. It covers essential concepts, techniques, and problem-solving strategies, making it suitable for beginners and those looking to strengthen their understanding. The text is structured to facilitate learning, with clear explanations and examples that illustrate the application of algebra in various contexts. Ideal for students, educators, and self-learners, it serves as a valuable resource for mastering algebraic fundamentals.

Algebraic specification techniques have become pivotal in computer science, particularly in the realms of abstract data types and software systems. This book presents a comprehensive theory that emphasizes core concepts, providing a well-motivated introduction to algebraic specification suitable for both computer scientists and mathematicians. It focuses on establishing precise definitions and formalizing computer science concepts mathematically, serving as a foundational resource for teaching, research, and development in algebraic techniques and their applications in programming and system design.

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.

This book constitutes the refereed proceedings of the 4th International Conference on Graph Transformations, ICGT 2008, held in Leicester, UK, in September 2008. The 27 revised full papers presented together with 5 tutorial and workshop papers and 3 invited lectures were carefully selected from 57 submissions. All current aspects in graph drawing are addressed including hypergraphs and termgraph rewriting, applications of graph transformation, execution of graph transformations, compositional systems, validation and verification, graph languages and special transformation concepts, as well as patterns and model transformations. In addition the volume contains 17 short papers of the ICGT 2008 Doctoral Symposium.

Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool environment. Finally the appendix covers the basics of category theory, signatures and algebras. The book addresses both research scientists and graduate students in computer science, mathematics and engineering.

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.

This book constitutes the refereed proceedings of the Second International Conference on Graph Transformation, ICGT 2004, held in Rome, Italy, in September/October 2004. The 26 revised full papers presented together with three invited contributions and summaries of 2 tutorials and 5 workshops were carefully reviewed and selected from 58 submissions. The papers are organized in topical sections on integration technology, chemistry and biology, graph transformation concepts, DPO theory for high-level structures, analysis and testing, graph theory and algorithms, application conditions and logic, transformation of special structures, and object-orientation.