Matrix Graph Grammars

TL;DR

This work aims to develop an algebraic framework for graph grammars, specifically Matrix Graph Grammars, to better understand graph dynamics and generalize formal language concepts.

Contribution

It introduces an algebraic approach to graph grammars, extending the theoretical foundation and analysis techniques for graph dynamics.

Findings

Proposes an algebraic formalization of graph grammars

Provides a new perspective on graph dynamics and transformations

Lays groundwork for further analysis and generalizations

Abstract

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.