Matrix Graph Grammars as a Model of Computation

TL;DR

This paper explores Matrix Graph Grammars (MGG) as a formal model of computation, analyzing its relation to Turing machines and Boolean circuits to advance complexity theory.

Contribution

It introduces MGG as a formal grammar and computational model, connecting it with established models like TMs and BCs for the first time.

Findings

MGG can simulate Turing machines and Boolean circuits

Techniques for MGG are applicable to other models

MGG provides a new perspective on graph dynamics and computation

Abstract

Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of tackling complexity theory through MGG. We also study its relation with other well-known models such as Turing machines (TM) and Boolean circuits (BC) as well as non-determinism. As a side effect, all techniques available for MGG can be applied to TMs and BCs.