Introduction to the algebraic theory of graph grammars (a survey)

Abstract

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. The complete material is illustrated by several examples, especially by applications to a "very small data base system", where consistent states are represented as graphs, operation rules and operations as productions and derivations in a graph grammar respectively. Further applications to recursively defined functions, record handling, compiler techniques and development and evolution in Biology are sketched in the introduction. This survey is divided into the following sections:

• 1. INTRODUCTION

• 2. GLUING CONSTRUCTIONS FOR GRAPHS

• 3. SEQUENTIAL GRAPH GRAMMARS

• 4. CHURCH-ROSSER PROPERTIES, PARALLELISM — AND CONCURRENCY THEOREMS

• 5. PROPERTIES OF DERIVATION SEQUENCES

• 6. PARALLEL GRAPH GRAMMARS

• 7. LOCALLY STAR GLUING FORMULAS

• 8. GRAPH LANGUAGES

• 9. APPENDIUM: CONCEPTS OF CATEGORY THEORY USED IN THE ALGEBRAIC THEORY OF GRAPH GRAMMARS

• 10. REFERENCES