This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and… Expand

The aim of this survey is to motivate and introduce the basic constructions and results which have been developed in the algebraic theory of graph grammars up to now, as well as applications to a "very small data base system", where consistent states are represented as graphs.Expand

An algebraic theory of graph-grammars is presented using homomorphisms and pushout-constructions to specify embeddings and direct derivations constructively and allows simplification of the proofs and pregnant formulation of concepts like "parallel composition" and "translation of grammars".Expand

The aim of this book is to present fundamentals of algebraic specifications with respect to the following three aspects: fundamentals in the sense of a carefully motivated introduction to algebraic… Expand

data type in the sense of Hoare describes the class of admissible representations (or implementations), that a specification should define such a class rather than a single algebra, and that the… Expand

This chapter starts with an overwiev of the basic notions common to the two algebraic approaches, the "double-pushout (DPO) approach) and the "single-push out (SPO) approaches"; next it is presented the classical theory and some recent development of the double- pushout approach.Expand

A rigorous approach to typed attributed graph transformation is obtained, providing as fundamental results the Local Church-Rosser, Parallelism, Concurrency, Embedding and Extension Theorem and a Local Confluence Theorem known as Critical Pair Lemma in the literature.Expand