Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach

Corradini, Andrea and Montanari, Ugo and Rossi, Francesca and Ehrig, H. and Heckel, Reiko and Loewe, M. (1996) Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

Postscript (GZip) - Published Version Available under License Creative Commons Attribution No Derivatives. Download (585Kb)

Abstract

The algebraic approaches to graph transformation are based on the concept of gluing of graphs, modelled by pushouts in suitable categories of graphs and graph morphisms. This allows one not only to give 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 this chapter we start with an overwiev of the basic notions common to the two algebraic approaches, the "double-pushout (DPO) approach" and the "single-pushout (SPO) approach"; next we present the classical theory and some recent development of the double-pushout approach. The next chapter is devoted instead to the single-pushout approach, and it is closed by a comparison between the two approaches. -- This document will appear as a chapter of the "The Handbook of Graph Grammars. Volume I: Foundations" , G. Rozenberg (Ed.), World Scientific.

Repository staff only actions