{"title":"Monographs In Theoretical Computer Science An Eatcs Series","description":null,"products":[{"product_id":"fundamentals-of-algebraic-graph-transformation-book-hartmut-ehrig-9783540311874","title":"Fundamentals of Algebraic Graph Transformation","description":"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.   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It shows how CP-nets have been de­ veloped - from being a promising theoretical model to being a full-fledged lan­ guage for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and\/or com­ puters communicate by means of some more or less formal rules). The book contains the formal definition of CP-nets and the mathematical theory behind their analysis methods. However, it has been the intention to write the book in such a way that it also becomes attractive to readers who are more interested in applications than the underlying mathematics. This means that a large part of the book is written in a style which is closer to an engineering textbook (or a users' manual) than it is to a typical textbook in theoretical computer science. The book consists of three separate volumes. 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Moreover, it has become apparent that among the great variety of computer technologies available to potential users a crucial role will be played by concurrent systems. The reason is that many commonly occurring phenomena and computer applications are highly con­ current : typical examples include control systems, computer networks, digital hardware, business computing, and multimedia systems. Such systems are characterised by ever increasing complexity, which results when large num­ bers of concurrently active components interact. This has been recognised and addressed within the computing science community. In particular, sev­ eral form al models of concurrent systems have been proposed, studied, and applied in practice. This book brings together two of the most widely used formalisms for de­ scribing and analysing concurrent systems: Petri nets and process algebras. 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The most natural and appropriate formalism for dealing with string rewriting is the notion of a semi-Thue system and this monograph treats its central aspects. The reduction relation is here defined firstly by the direction of the rules and secondly by some metric that yields efficient algorithms. These systems are general enough to discuss the basic notions of arbitrary replacement systems, such as termination, confluence, and the Church-Rosser property in its original meaning. Confluent semi-Thue systems in which each and every derivation consists of finitely many steps only are called complete; they guarantee the existence of unique normal forms as canonical representatives of the Thue congruence classes. Each such system can be considered a nondeterministic algorithm for the word problem which works correctly without backtracking. This is often conceptually simpler and more elegant than an ad hoc construction. 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They offer a gentle introduction to the basics of the method, and in particular they detail an unfolding-based algorithm for model checking concurrent systems against properties specified as formulas of linear temporal logic (LTL). Self-contained chapters cover transition systems and their products; unfolding products; search procedures for basic verification problems, such as reachability and livelocks; and model checking LTL. The final chapter summarizes the results of the book, and points the reader to tools and case studies.   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