Graph Field Automata

TL;DR

This paper introduces Graph Field Automata, a new formalism that extends Matrix Graph Grammars to provide a framework for machines capable of graph rewriting using algebraic methods.

Contribution

It presents the dual of Matrix Graph Grammars and extends this formalism to develop Graph Field Automata, enabling new machine models for graph rewriting.

Findings

Introduces Graph Field Automata as a dual to Matrix Graph Grammars.

Provides a formal framework for graph-based machine models.

Extends algebraic graph rewriting systems.

Abstract

The Graph Automata have been the paradigm in the expression of utilizing Graphs as a language. Matrix Graph grammars \cite{Pedro} are an algebratization of graph rewriting systems. Here we present the dual of this formalizm which some extensions which we term Graph Field Automata The advantage to this approach is a framework for expressing machines that can use Matrix Graph Grammars.